Relevant bibliographies by topics / Degenerate PDE

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Degenerate PDE'

Author: Grafiati
Published: 10 August 2024

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Journal articles on the topic "Degenerate PDE"

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Rocca, Elisabetta, and Riccarda Rossi. "A degenerating PDE system for phase transitions and damage." Mathematical Models and Methods in Applied Sciences 24, no. 07 (April 14, 2014): 1265–341. http://dx.doi.org/10.1142/s021820251450002x.

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In this paper, we analyze a PDE system arising in the modeling of phase transition and damage phenomena in thermoviscoelastic materials. The resulting evolution equations in the unknowns ϑ (absolute temperature), u (displacement), and χ (phase/damage parameter) are strongly nonlinearly coupled. Moreover, the momentum equation for u contains χ-dependent elliptic operators, which degenerate at the pure phases (corresponding to the values χ = 0 and χ = 1), making the whole system degenerate. That is why, we have to resort to a suitable weak solvability notion for the analysis of the problem: it consists of the weak formulations of the heat and momentum equation, and, for the phase/damage parameter χ, of a generalization of the principle of virtual powers, partially mutuated from the theory of rate-independent damage processes. To prove an existence result for this weak formulation, an approximating problem is introduced, where the elliptic degeneracy of the displacement equation is ruled out: in the framework of damage models, this corresponds to allowing for partial damage only. For such an approximate system, global-in-time existence and well-posedness results are established in various cases. Then, the passage to the limit to the degenerate system is performed via suitable variational techniques.
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Nytrebych, Zinovii, and Oksana Malanchuk. "The conditions of existence of a solution of the degenerate two-point in time problem for PDE." Asian-European Journal of Mathematics 12, no. 03 (May 27, 2019): 1950037. http://dx.doi.org/10.1142/s1793557119500372.

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The problem with local nonhomogeneous two-point in time conditions for homogeneous PDE of the second order in time and, generally, infinite order in spatial variables is investigated. This problem is degenerated namely its characteristic determinant is identically zero. The condition of existence of a solution of the degenerate problem is established. Also, we proposed the differential-symbol method of constructing the solution of the problem in the classes of entire functions. Some examples of solving the degenerate two-point in time problems are presented.
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Kubo, Masahiro, and Quqin Lu. "Evolution equations for nonlinear degenerate parabolic PDE." Nonlinear Analysis: Theory, Methods & Applications 64, no. 8 (April 2006): 1849–59. http://dx.doi.org/10.1016/j.na.2005.07.027.

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Spence, S., G. Rena, G. Sweeney, and M. D. Houslay. "Induction of Ca2+/calmodulin-stimulated cyclic AMP phosphodiesterase (PDE1) activity in Chinese hamster ovary cells (CHO) by phorbol 12-myristate 13-acetate and by the selective overexpression of protein kinase C isoforms." Biochemical Journal 310, no. 3 (September 15, 1995): 975–82. http://dx.doi.org/10.1042/bj3100975.

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The cAMP phosphodiesterase (PDE) activity of CHO cells was unaffected by the addition of Ca2+ +calmodulin (CaM), indicating the absence of any PDE1 (Ca2+/CaM-stimulated PDE) activity. Treatment with the tumour promoting phorbol ester phorbol 12-myristate 13-acetate (PMA) led to the rapid transient induction of PDE1 activity which attained a maximum value after about 13 h before slowly decreasing. Such induction was attenuated by actinomycin D. PCR primers were designed to hybridize with two regions identified as being characteristic of PDE1 forms found in various species and predicted to amplify a 601 bp fragment. RT-PCR using degenerate primers allowed an approx. 600 bp fragment to be amplified from RNA preparations of rat brain but not from CHO cells unless they had been treated with PMA. CHO cells transfected to overexpress protein kinase C (PKC)-alpha and PKC-epsilon, but not those transfected to overexpress PKC-beta I or PKC-gamma, exhibited a twofold higher PDE activity. They also expressed a PDE1 activity, with Ca2+/CaM effecting a 1.8-2.8-fold increase in total PDE activity. RT-PCR, with PDE1-specific primers, identified an approx. 600 bp product in CHO cells transfected to overexpress PKC-alpha and PKC-epsilon, but not in those overexpressing PKC-beta I or PKC-gamma. Treatment of PKC-alpha transfected cells with PMA caused a rapid, albeit transient, increase in PDE1 activity, which reached a maximum some 1 h after PMA challenge, before returning to resting levels some 2 h later. The residual isobutylmethylxanthine (IBMX)-insensitive PDE activity was dramatically reduced (approx. 4-fold) in the PKC-gamma transfectants, suggesting that the activity of the cyclic AMP-specific IBMX-insensitive PDE7 activity was selectively reduced by overexpression of this particular PKC isoform. These data identify a novel point of ‘cross-talk’ between the lipid and cyclic AMP signalling systems where the action of specific PKC isoforms is shown to cause the induction of Ca2+/CaM-stimulated PDE (PDE1) activity. It is suggested that this protein kinase C-mediated process might involve regulation of PDE1 gene expression by the AP-1 (fos/jun) system.
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PARDOUX, ÉTIENNE, and AHMADOU BAMBA SOW. "HOMOGENIZATION OF A PERIODIC DEGENERATE SEMILINEAR ELLIPTIC PDE." Stochastics and Dynamics 11, no. 02n03 (September 2011): 475–93. http://dx.doi.org/10.1142/s0219493711003401.

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In this paper, a semilinear elliptic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of ℝd. Our fully probabilistic method is based on the connection between PDEs and BSDEs with random terminal time and the weak convergence of a class of diffusion processes.
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Elshegmani, Zieneb Ali, and Rokiah Rozita Ahmad. "Fourier Transform of the Continuous Arithmetic Asian Options PDE." ISRN Applied Mathematics 2011 (September 26, 2011): 1–8. http://dx.doi.org/10.5402/2011/643749.

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Price of the arithmetic Asian options is not known in a closed-form solution, since arithmetic Asian option PDE is a degenerate partial differential equation in three dimensions. In this work we provide a new method for computing the continuous arithmetic Asian option price by means of partial differential equations. Using Fourier transform and changing some variables of the PDE we get a new direct method for solving the governing PDE without reducing the dimensionality of the PDE as most authors have done. We transform the second-order PDE with nonconstant coefficients to the first order with constant coefficients, which can be solved analytically.
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Katzourakis, Nikos. "On linear degenerate elliptic PDE systems with constant coefficients." Advances in Calculus of Variations 9, no. 3 (July 1, 2016): 283–91. http://dx.doi.org/10.1515/acv-2015-0004.

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AbstractLet ${\mathbf{A}}$ be a symmetric convex quadratic form on ${\mathbb{R}^{Nn}}$ and Ω $\subset$$\mathbb{R}^{n}$ a bounded convex domain. We consider the problem of existence of solutions u: Ω $\subset$$\mathbb{R}^{n}$$\to$$\mathbb{R}^{N}$ to the problem${}\left\{\begin{aligned} \displaystyle\sum_{\beta=1}^{N}\sum_{i,j=1}^{n}% \mathbf{A}_{\alpha i\beta j}D^{2}_{ij}u_{\beta}&\displaystyle=f_{\alpha}&&% \displaystyle\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\text{on }\partial\Omega,\end{% aligned}\right.\phantom{\}}$when ${f\in L^{2}(\Omega,\mathbb{R}^{N})}$. Problem (1) is degenerate elliptic and it has not been considered before without the assumption of strict rank-one convexity. In general, it may not have even distributional solutions. By introducing an extension of distributions adapted to (1), we prove existence, partial regularity and by imposing an extra condition uniqueness as well. The satisfaction of the boundary condition is also an issue due to the low regularity of the solution. The motivation to study (1) and the method of the proof arose from recent work of the author [10] on generalised solutions for fully nonlinear systems.
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Biswas, Imran H., Espen R. Jakobsen, and Kenneth H. Karlsen. "Difference-Quadrature Schemes for Nonlinear Degenerate Parabolic Integro-PDE." SIAM Journal on Numerical Analysis 48, no. 3 (January 2010): 1110–35. http://dx.doi.org/10.1137/090761501.

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Antil, Harbir, and Shawn W. Walker. "Optimal Control of a Degenerate PDE for Surface Shape." Applied Mathematics & Optimization 78, no. 2 (March 16, 2017): 297–328. http://dx.doi.org/10.1007/s00245-017-9407-3.

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Ivochkina, Nina, Neil Trudinger, and Xu-Jia Wang. "The Dirichlet Problem for Degenerate Hessian Equations." Communications in Partial Differential Equations 29, no. 1-2 (January 2005): 219–35. http://dx.doi.org/10.1081/pde-120028851.

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Dissertations / Theses on the topic "Degenerate PDE"

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Hatami, Farhad. "Configurations of Wardrop's equilibrium and application to traffic analysis." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/565891.

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This thesis consists of two parts, and the connection between them is the so-called Wardrop's equilibrium. In the rst part of this thesis, which is the theoretical part, we study the congested transport dynamics arising from a non-autonomous tra c optimization problem. In this setting, we prove one can nd an optimal tra c strategy with support on the trajectories of a DiPerna-Lions ow. The proof follows the scheme introduced by Brasco, Carlier and Santambrogio in the autonomous setting, applied to the case of supercritical Sobolev dependence in the spatial variable. This requires both Lipschitz and weighted Sobolev apriori bounds for the minimizers of a class of integral functionals whose ellipticity bounds are satis ed only away from a ball of the gradient variable. We are then able to nd the con guration of Wardrop's equilibrium. In the second part of this thesis, which is the practical part, we use the established Wardrop's equi- librium in the theoretical section, in order to optimize the tra c problem in rel-life application. New OD demand problem formulation is explored which allows the modeler to de ne structural similarity between the historical and estimated OD matrix while ensuring computationally fast and tractable solution. Shrinkage regression methods, such as Ridge and Lasso regression, are proposed to de ne distance function between historical and estimated OD matrix, in order to minimize estimation vari- ance, and ensure the estimated OD matrix is close to true value. The presented OD estimation models reduce dimensionality of the OD demand vector, which is crucial when the dimensionality of OD ma- trix is high, due to high level of zoning system. A new solution approach based on the well-known gradient descent algorithm is applied to solve the proposed models. Finally, results are tested out on a real life-size network.
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Gerencsér, Máté. "Stochastic PDEs with extremal properties." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20445.

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We consider linear and semilinear stochastic partial differential equations that in some sense can be viewed as being at the "endpoints" of the classical variational theory by Krylov and Rozovskii [25]. In terms of regularity of the coeffcients, the minimal assumption is boundedness and measurability, and a unique L2- valued solution is then readily available. We investigate its further properties, such as higher order integrability, boundedness, and continuity. The other class of equations considered here are the ones whose leading operators do not satisfy the strong coercivity condition, but only a degenerate version of it, and therefore are not covered by the classical theory. We derive solvability in Wmp spaces and also discuss their numerical approximation through finite different schemes.
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Grundling, Hendrik. "Algebraic structure of degenerate systems /." Title page, table of contents and summary only, 1986. http://web4.library.adelaide.edu.au/theses/09PH/09phg888.pdf.

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Moss, Jonathan. "Linear degeneracy in multidimensions." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/20171.

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Linear degeneracy of a PDE is a concept that is related to a number of interesting geometric constructions. We first take a quadratic line complex, which is a three parameter family of lines in projective space P3 specified by a single quadratic relation in the Plucker coordinates. This complex supplies us with a conformal structure in P3. With this conformal structure, we associate a three-dimensional second order quasilinear wave equation. We show that any PDE arising in this way is linearly degenerate, furthermore, any linearly degenerate PDE can be obtained by this construction. We classify Segre types of quadratic complexes for which the structure is conformally flat, as well as Segre types for which the corresponding PDE is integrable. These results were published in [1]. We then introduce the notion of characteristic integrals, discuss characteristic integrals in 3D and show that, for certain classes of second-order linearly degenerate dispersionless integrable PDEs, the corresponding characteristic integrals are parameterised by points on the Veronese variety. These results were published in [2].
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Branco, Meireles Joao. "Singular Perturbations and Ergodic Problems for degenerate parabolic Bellman PDEs in R^m with Unbounded Data." Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3424194.

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In this thesis we treat the first singular perturbation problem of a stochastic model with unbounded and controlled fast variables with success. Our methods are based on the theory of viscosity solutions, homogenisation of fully nonlinear PDEs and a careful analysis of the associated ergodic stochastic control problem in the whole space R^m. The text is divided in two parts. In the first chapter, we investigate the existence and uniqueness as well as a suitable stability of the solution to the associated ergodic problem that are crucial to characterize the effective Hamiltonian of the limit (effective) Cauchy problem in Chapter II of this thesis. The main achievement obtained in this part is a purely analytical proof for the uniqueness of solution to such ergodic problem. Since the state space of the problem is not compact, in general there are infinitely many solutions to the ergodic problem. However, if one restrict the class of solutions to the set of bounded-below functions, then it is known that uniqueness holds up to an additive constant. The existing proof relies on some probabilistic techniques employing the invariant probability measure for the associated stochastic process. Here we give a new proof, purely analytic, based on the strong maximum principle. We believe that our results can be interesting and useful for researchers in the PDE community. In the second chapter, we introduce our singular perturbation model of a stochastic control problem and we prove our main result: the convergence of the value function $V^\epsilon$ associated to the problem to the solution of the limiting equation. More precisely, we prove that the functions \underline{V} (t,x):=\liminf_{(\epsilon,t',x') \to (0,t,x)} \inf_{y \in \mathbb{R}^m} V^\epsilon (t',x',y) and \bar{V} (t,x) :=(\sup_{R} \bar{V}_R)^* (t,x) \text{ (upper semi-continuous envelope of $\sup_{R} \bar{V}_R$ )} where $\bar{V}_{R} (t,x):=\limsup_{(\epsilon, t',x') \to (0,t,x)} \sup_{y \in B_R (0)} V^\epsilon (t',x',y)$, are, respectively, a super and a subsolution of the effective Cauchy problem. As a corollary of this result, $V^\epsilon$ converges to the unique solution $V$ of the effective equation provided the equation admits the comparison principle for discontinuous viscosity solutions. The justification of this convergence is not trivial at all. It especially involves some regularity issues and a careful treatment of viscosity techniques and stochastic analysis. This result has never been obtained before.
In questa tesi viene trattato con successo il primo problema di perturbazione singolare di un modello stocastico con variabili veloci controllate e non limitate. I metodi si basano sulla teoria delle soluzioni di viscosità, omogeinizzazione dei PDE completamente non lineari, e su un'attenta analisi del problema stocastico ergodico associato, valido nell'intero spazio R^m. Il testo è diviso in due parti. Nel primo capitolo, saranno studiate l'esistenza, l'unicità e alcune proprietà di stabilità della soluzione del problema ergodico, riferito sopra, che sono essenziali per caratterizzare il Hamiltoniano effettivo che appare in un Problema di Cauchy "limite", che sarà descritto nel capitolo II di questa tesi. Il principale contributo, presentato in questa parte, è una prova puramente analitica dell'unicità della soluzione di questo problema ergodico. Siccome lo stato dello spazio del problema non è compatto, in generale ci sono un numero infinito di soluzioni a questo problema. Tuttavia, se uno limitasse la classe di soluzioni all'insieme di funzioni limitate inferiormente, allora è noto che l'unicità sarà mantenuta a meno di una costante. La prova esistente si basa su alcune tecniche probabilistiche che impiegano la misura di probabilità invariante per l'associato processo stocastico. Qua verrà data una nuova prova, puramente analitica, basata sul principio del massimo. Si ritiene che il risultato potrà essere interessante ed utile per i ricercatori che lavorano all'interno della comunità di ricerca delle Equazioni Differenziali alle derivate Parziali (PDE). Nel secondo capitolo, sarà introdotto un modello di perturbazione singolare di un problema di controllo stocastico, e provato il risultato principale: la convergenza della funzione valore $V^\epsilon$, associata al nostro problema, per soluzione dell'equazione limite. Più precisamente, sarà provato che le funzioni: \underline{V} (t,x):=\liminf_{(\epsilon,t',x') \to (0,t,x)} \inf_{y \in \mathbb{R}^m} V^\epsilon (t',x',y) e \bar{V} (t,x) :=(\sup_{R} \bar{V}_R)^* (t,x) \text{ (upper semi-continuous envelope of $\sup_{R} \bar{V}_R$ )} dove $\bar{V}_{R} (t,x):=\limsup_{(\epsilon, t',x') \to (0,t,x)} \sup_{y \in B_R (0)} V^\epsilon (t',x',y)$, sono, rispettivamente, una super soluzione e una sottosoluzione del problema effettivo di Cauchy. Come corollario di questo risultato, $V^\epsilon$ converge all'unica soluzione V della equazione effettiva se l'equazione limite permette il principio di comparazione per le soluzioni di viscosità discontinue. La motivazione di questa convergenza non è ovvia del tutto. Coinvolge specialmente alcuni problemi di regolarità e un trattamento attento delle tecniche di viscosità e di analisi stocastica. Questo risultato è nuovo e non è mai stato ottenuto, prima d'ora, nella letteratura Matematica.
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Peillon, Etienne. "Simulation and analysis of sign-changing Maxwell’s equations in cold plasma." Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAE004.

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De nos jours, les plasmas sont principalement utilisés à des fins industrielles. L'un des exemples les plus fréquemment cités d'utilisation industrielle est la production d'énergie électrique via des réacteurs nucléaires à fusion. Pour contenir le plasma correctement à l'intérieur du réacteur, un champ magnétique est imposé en arrière-plan, et la densité et la température du plasma doivent être précisément contrôlées. Cela est effectué en envoyant des ondes électromagnétiques à des fréquences et dans des directions spécifiques en fonction des caractéristiques du plasma.La première partie de cette thèse de doctorat est consacrée à l'étude du modèle du plasma avec un fort champ magnétique en arrière-plan, ce qui correspond à un métamatériau hyperbolique. L'objectif est d'étendre les résultats existant en 2D au cas 3D et de dériver une condition de radiation. Nous introduisons une séparation des champs électriques et magnétiques ressemblant à la décomposition TE et TM habituelle, puis nous présentons quelques résultats sur les deux problèmes résultants. Les résultats sont dans un état très partiel et constituent un brouillon approximatif sur le sujet.La deuxième partie étudie l'EDP dégénérée associée aux ondes résonantes « lower-hybrid » dans le plasma. Le problème aux limites associé est bien posé dans un cadre variationnel « naturel ». Cependant, ce cadre n'inclut pas le comportement singulier présenté par les solutions physiques obtenues via le principe d'absorption limite. Ce comportement singulier est important du point de vue physique car il induit le chauffage du plasma mentionné précédemment. Un des résultats clés de cette deuxième partie est la définition d'une notion de saut à travers l'interface à l'intérieur du domaine, ce qui permet de caractériser la décomposition de la solution d'absorption limite en parties régulière et singulière
Nowadays, plasmas are mainly used for industrial purpose. One of the most frequently cited examples of industrial use is electric energy production via fusion nuclear reactors. Then, in order to contain plasma properly inside the reactor, a background magnetic field is imposed, and the density and temperature of the plasma must be precisely controlled. This is done by sending electromagnetic waves at specific frequencies and directions depending on the characteristics of the plasma.The first part of this PhD thesis consists in the study of the model of plasma in a strong background magnetic field, which corresponds to a hyperbolic metamaterial. The objective is to extend the existing results in 2D to the 3D-case and to derive a radiation condition. We introduce a splitting of the electric and magnetic fields resembling the usual TE and TM decomposition, then, it gives some results on the two resulting problems. The results are in a very partial state, and constitute a rough draft on the subject.The second part consists in the study of the degenerate PDE associated to the lower-hybrid resonant waves in plasma. The associated boundary-value problem is well-posed within a ``natural'' variational framework. However, this framework does not include the singular behavior presented by the physical solutions obtained via the limiting absorption principle. Notice that this singular behavior is important from the physical point of view since it induces the plasma heating mentioned before. One of the key results of this second part is the definition of a notion of weak jump through the interface inside the domain, which allows to characterize the decomposition of the limiting absorption solution into a regular and a singular parts
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Ikeda, Katsumoto. "Magnetothermoelectric properties of the degenerate semiconductor Hg1-xFexSe." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ53000.pdf.

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Maizurna, Isna. "Semigroup methods for degenerate cauchy problems and stochastic evolution equations /." Title page, abstract and contents only, 1999. http://web4.library.adelaide.edu.au/theses/09PH/09phm2328.pdf.

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Zhan, Yi. "Viscosity solutions of nonlinear degenerate parabolic equations and several applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ49931.pdf.

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Hiller, Christine Louise. "'Daddy's girls', 'degenerate daughters', tracing interconnected violences within women's 'survivor' narratives." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0001/MQ40649.pdf.

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Books on the topic "Degenerate PDE"

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The method of intrinsic scaling: A systematic approach to regularity for degenerate and singular PDEs. Berlin: Springer, 2008.

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Urbano, José Miguel. The Method of Intrinsic Scaling: A Systematic Approach to Regularity for Degenerate and Singular PDEs (Lecture Notes in Mathematics Book 1930). Springer, 2008.

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Alexandrowicz, C. H. The Partition of Africa by Treaty (1974). Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780198766070.003.0020.

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This chapter analyses the partition of the African continent via treaties. It begins with an introductory examination of pre-nineteenth-century European–African treaty-making and references some classic writers to Africa. It then discusses relevant documents on the ‘scramble’ for titles to African territory. These demonstrate the extent to which normal institutions of the law of nations as originally applied to European–African relations degenerated into instruments of colonial penetration in the second half of the nineteenth century, particularly after the Berlin Conference of 1884–85, which led to a multilaterally conceived plan of partition of the whole continent. Partition took place in two phases, i.e. the transfer of legal titles to territory from the African transferor to the European transferee wherein the ruler still played an active part, and then the absorption of territory by annexation. Effective occupation by the Europeans usually came much later than the acquisition of legal title.
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Shahane, Shantanu. Osteoarthritis of the elbow joint. Oxford University Press, 2011. http://dx.doi.org/10.1093/med/9780199550647.003.005.005.

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♦ Symptomatic, primary osteoarthritis of the elbow usually occurs in young men involved in heavy manual labour.♦ Common causes of secondary osteoarthritis of the elbow are trauma, infection, bleeding disorders and neuropathic conditions.♦ Clinically, the commonest presenting symptom is loss of motion. Patients can also complain of pain, locking and ulnar nerve symptoms.♦ Plain X-rays are usually sufficient for diagnosis. They show reduction in joint space and osteophytes at the tip of olecranon and coronoid processes. Loose bodies are also frequently seen.♦ Symptoms in early stages of arthritis are controlled by nonoperative means. Steroids are rarely used in clinical practice.♦ In advanced cases, numerous operative treatments including arthroscopic and open procedures are available.♦ Total Elbow replacement (TER) for primary degenerative arthritis of the elbow is only to be considered as the last option and when stringent pre and post-operative requirements are followed.
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Flower, Oliver, and Matthew Mac Partlin. Pathophysiology, causes, and management of non-traumatic spinal injury. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199600830.003.0242.

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Non-traumatic spinal cord injury (NTSCI) is at least as common as traumatic spinal cord injury (TSCI). It affects both sexes equally and an older population than TSCI. It is a devastating condition with immense functional implications for the individuals involved. There is a wide spectrum of aetiologies with varying pathophysiology and knowledge of these is important to avoid delay in diagnosis and time-critical treatment. The most common causes described in case series in developed countries are degenerative disc disease, canal stenosis, tumours, vascular diseases and inflammatory conditions. History and examination may help direct investigations, but magnetic resonance imaging is usually required. Management of NTSCI focuses on diagnosing and treating the precipitating cause, supportive management, and preventing complications. The outcomes of non-traumatic spinal cord injury are similar to those of traumatic spinal cord injury and depend on the grade and level of injury, pre-morbid status, and concurrent co-morbidities.
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Baglietto-Vargas, David, Rahasson R. Ager, Rodrigo Medeiros, and Frank M. LaFerla. Animal Models of Neurodegenerative Diseases. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780190233563.003.0014.

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The incidence and prevalence of neurodegenerative disorders (e.g., Alzheimer’s disease (AD), Parkinson’s disease (PD), and Huntington’s disease (HD), etc.) are growing rapidly due to increasing life expectancy. Researchers over the past two decades have focused their efforts on the development of animal models to dissect the molecular mechanisms underlying neurodegenerative disorders. Existing models, however, do not fully replicate the symptomatic and pathological features of human diseases. This chapter focuses on animal models of AD, as this disorder is the most prevalent of the brain degenerative conditions afflicting society. In particular, it briefly discusses the current leading animal models, the translational relevance of the preclinical studies using such models, and the limitations and shortcomings of using animals to model human disease. It concludes with a discussion of potential means to improve future models to better recapitulate human conditions.
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Book chapters on the topic "Degenerate PDE"

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Rabinowitz, Paul H. "Multibump Solutions of a Semilinear Elliptic PDE on Rn." In Degenerate Diffusions, 175–85. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0885-3_12.

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Efendiev, Messoud. "ODE-PDE coupling arising in the modelling of a forest ecosystem." In Attractors for Degenerate Parabolic Type Equations, 191–212. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/11.

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Efendiev, Messoud. "On a class of PDEs with degenerate diffusion and chemotaxis: Autonomous case." In Attractors for Degenerate Parabolic Type Equations, 147–72. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/09.

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Efendiev, Messoud. "On a class of PDEs with degenerate diffusion and chemotaxis: Nonautonomous case." In Attractors for Degenerate Parabolic Type Equations, 173–90. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/10.

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Teixeira, Eduardo V., and José Miguel Urbano. "Geometric Tangential Analysis and Sharp Regularity for Degenerate pdes." In Harnack Inequalities and Nonlinear Operators, 175–92. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73778-8_9.

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Düzgün, Fatma Gamze, Sunra Mosconi, and Vincenzo Vespri. "Harnack and Pointwise Estimates for Degenerate or Singular Parabolic Equations." In Contemporary Research in Elliptic PDEs and Related Topics, 301–68. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18921-1_8.

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Andreianov, Boris. "Time Compactness Tools for Discretized Evolution Equations and Applications to Degenerate Parabolic PDEs." In Finite Volumes for Complex Applications VI Problems & Perspectives, 21–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_3.

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Veske, A., U. Orth, K. Rüther, E. Zrenner, T. Rosenberg, W. Baehr, and A. Gal. "Mutations in the Gene for the B-Subunit of Rod Photoreceptor Cgmp-Specific Phosphodiesterase (PDEB) in Patients with Retinal Dystrophies and Dysfunctions." In Degenerative Diseases of the Retina, 313–22. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-1897-6_35.

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Nussbaum, M., I. Reider, and A. D. Korczyn. "Vascular Dementia (VD) and Primary Degenerative Dementia (PDD): Criteria for Differential Diagnosis." In Basic, Clinical, and Therapeutic Aspects of Alzheimer’s and Parkinson’s Diseases, 133–36. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-5847-3_28.

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Efendiev, Messoud, and Anna Zhigun. "On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension." In Recent Trends in Dynamical Systems, 179–203. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0451-6_9.

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Conference papers on the topic "Degenerate PDE"

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Ogawa, Takayoshi. "Decay and asymptotic behavior of solutions of the Keller–Segel system of degenerate and nondegenerate type." In Self-Similar Solutions of Nonlinear PDE. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc74-0-10.

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Pollmann, René, Franz Roeder, Victor Quiring, Raimund Ricken, Christof Eigner, Benjamin Brecht, and Christine Silberhorn. "Integrated bright broadband PDC source for quantum metrology." In Frontiers in Optics. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/fio.2022.jw5a.57.

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We demonstrate a broadband quantum light source employing non-degenerate type II parametric down conversion in a 40 mm long periodically poled LiNbO3 waveguide, pumped with a narrowband CW laser. Therefore maximising time frequency entanglement while maintaining high brightness.
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Fotsing, Yannick Kengne, and Xiaobo Tan. "Bias-Dependent Impedance Model for Ionic Polymer-Metal Composite Actuators." In ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/smasis2011-5011.

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Ionic polymer-metal composites (IPMCs) are a novel class of soft sensing and actuation materials with promising applications in robotic and biomedical systems. In this paper we present a model for nonlinear electrical dynamics of IPMC actuators, by applying perturbation analysis on the dynamics-governing partial differential equation (PDE) around a given bias voltage. By approximating the steady-state electric field under the bias with a piecewise linear function, we derive a linear PDE for the perturbed charge dynamics, which has piecewise constant coefficients and coefficients linear in the spatial variable. Through power series expansion, we solve the PDE to get the charge distribution up to any prescribed order. The perturbed electric field and current are subsequently obtained, which results in a bias-dependent impedance model. This model captures the nonlinear nature of the IPMC electrical dynamics, and degenerates to the linear model when the bias is zero. Simulation results are presented to illustrate the modeling approach.
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Shimizu, Shimpei, Takushi Kazama, Takeshi Umeki, Koji Enbutsu, Masanori Nakamura, Masashi Abe, Takayuki Kobayashi, and Yutaka Miyamoto. "PPLN-Based Polarization-Diverse Phase-Sensitive Amplification of 96-Gbaud PDM-PCS-64QAM Signal with Carrier-Phase-Locked Phase-Conjugated Twin Waves." In Optical Fiber Communication Conference. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/ofc.2024.th1f.3.

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We demonstrated non-degenerate phase-sensitive amplification (PSA) of a 96-Gbaud PDM-PCS-64QAM signal. Phase-conjugated twin waves (PCTWs) with a polarization-independent carrier phase provided low-noise PSA of a 2.5-dB black-box noise figure without polarization tracking of the PCTWs.
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Serkland, D. K., M. M. Fejer, R. L. Byer, and Y. Yamamoto. "Squeezed Vacuum Generation using a Quasiphasematched LiNbO3 Waveguide Parametric Amplifier." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/nlgw.1995.pd6.

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We have measured phase-sensitive amplification and quadrature squeezing using a quasiphasematched LiNbO3 waveguide degenerate parametric amplifier. We observed a 14% reduction in the noise in one quadrature, compared to the vacuum state, which is in quantitative agreement with our phase-sensitive amplification measurements.
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Russell, P. St J. "Nonlinear holography for wave-front conversion, frequency doubling, and parametric amplification." In Integrated Photonics Research. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/ipr.1990.wc5.

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When beams at frequencies ω0 and 2ω0 are mixed in a medium with third-order nonlinearity χ(3) a pattern of dc polarization fringes Pdc(3) results whose grating vector is K = kso − 2kpo, where kpo(r) and kso(r) are the wave vectors at ω0 and ω0. In germanosilicate optical fibers, Pdc(3) breaks the centrosymmetry of the amorphous core material (possibly by color-center alignment), creating a periodically modulated χ(2) = χ m (2)cos(K · r). This χ(2) structure automatically phase matches the fundamental light to its second harmonic (SH).1,2 Because the wave fronts of the participating beams do not have to be planar, the phenomenon may be labeled nonlinear holography.3 In a germanosilicate film waveguide, for example, a SH image beam at 2ω can be reconstructed, potentially with high efficiency, from a reference pump beam at ω ≈ ω0. Phase-matched degenerate parametric amplification of a complex signal wave front at ω is also possible, and in a ring cavity parametric oscillation would permit high-efficiency re-creation of a complex beam at ω.
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Flom, Steven R., J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi. "Fluence Dependent Dynamics Observed in the Resonant Third-Order Optical Response of C60 and C70 Films." In Nonlinear Optics. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.pd7.

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The fullerenes, C60 and C70, are molecules whose properties have been receiving increasing attention. Their high degree of symmetry and their three dimensional π—electron systems make them intriguing candidates for their potential nonlinear optical (NLO) properties. In order to investigate the resonant third—order optical response we have performed time resolved degenerate four—wave mixing (DFWM) experiments on films of pure C60 and pure C70 at 597 and 675 nm using an amplified ps laser system. The films were made by vapor deposition and characterized by FTIR and UV—Visible absorption spectroscopies.
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Medrano, C., M. Ingold, and P. Günter. "Self Pumped Phase Conjugation and Optical Light Oscillation in Fe Doped KNbO3." In Photorefractive Materials, Effects, and Devices II. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/pmed.1990.pd7.

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In recent years, self-pumped phase conjugation and self-induced photorefractive light oscillation have been reported, using different photorefractive materials. The main photorefractive materials used in these experiments are BaTiO3 and Bi12SiO20. In ferroelectric BaTiO3 the high electro-optic coefficients give rise to large reflectivities. In photoconductive and paraelectric Bi12SiO20 phase shifting techniques lead to enhanced self-diffracted intensities and phase conjugate reflectivities. KNbO3 is such a material which in addition to its high photorefractive sensitivity3 and large beam coupling gain4, has been shown to become highly photoconductive if prepared properly, leading to optimized response speed5 down to 100 μs. In a degenerate four wave mixing configuration, maximum phase conjugate reflectivities up to 25% with an applied electric field have been observed several years ago6. In a previous paper7 and for the first time, the possibility of using KNbO3 crystals for self-induced optical resonators has been reported. Both an unidirectional ring and a linear resonator configurations were realized and coherent light oscillations observed. Build up time constants of milliseconds were reported when an undoped reduced KNbO3 crystal was employed. However the measured phase conjugate reflectivity for these configurations were very small. Later on self-pumped phase conjugation in KNbO3 has been reported at 124°C8. In this paper we report on self-pumped phase conjugation experiments, performed with an iron doped KNbO3 crystal at room temperature in both a linear and a passive ring resonator configuration. We also report on self-pumped phase conjugation in a configuration requiring no external optical elements. Results deriving from degenerate four-wave mixing are also presented.
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Cook, Daniel J., Matthew S. Yeager, and Boyle C. Cheng. "Facet Translation Analysis in the Lumbar Spine: An Application in Posterior Dynamic Stabilization." In ASME 2012 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/sbc2012-80319.

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Facet articulation in the human lumbar spine has not been thoroughly characterized with regard to the effects of degeneration or surgical intervention. Kozanek et al. investigated the translation and rotation of the facets in 11 healthy adult subjects during maximal voluntary bending [1]. Li et al. used the same measurement technique on a cohort of 10 patients with degenerative disc disease (DDD) and found some significant differences in facet motion compared to a cohort of healthy patients [2]. Jegapragasan et al. investigated facet translations in intact lumbar spines in vitro and found the technique of facet translation analysis (FTA) to yield significantly different results compared to a similar analysis based on a vertebral body based coordinate system [3]. This abstract describes the application of this FTA technique in evaluating a posterior dynamic stabilization (PDS) system.
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Reports on the topic "Degenerate PDE"

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Wang, Xiao, Hong Shen, Yujie Liang, Yixin Wang, Meiqi Zhang, and Hongtao Ma. Effectiveness of Tango Intervention on Motor Symptoms in Patients with Parkinson's Disease: A Protocol for Systematic Review and Meta-Analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, May 2022. http://dx.doi.org/10.37766/inplasy2022.5.0009.

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Review question / Objective: Parkinson's disease (PD) is a degenerative neurological disease caused by the loss of dopaminergic neurons in the pars compacta of the substantia nigra of the brain, resulting in lesions in the basal ganglia. The main motor symptoms of PD include resting tremor, rigidity, akinesia or bradykinesia and postural instability. As an exercise intervention based on musical accompaniment, tango dance has shown positive effects on the rehabilitation of motor symptoms in PD patients in recently. In this study, we systematically reviewed the efficacy of tango intervention in alleviating the motor symptoms of patients with PD. Condition being studied: Parkinson. Information sources: The following electronic databases will be searched: PubMed, Cochrane Central Register of Controlled Trials (CENTRAL), Web of Science Core collection, and China National Knowledge Infrastructure Database (CNKI) and WanFang Database.
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Ni, Jiachun, Qiong Jiang, Gang Mao, Yi Yang, Qin Wei, Changcheng Hou, Xiangdong Yang, Wenbin Fan, and Zengjin Cai. The effectiveness and safety of acupuncture for constipation associated with Parkinson’s disease: Protocol for a systematic review and meta-analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, February 2022. http://dx.doi.org/10.37766/inplasy2022.2.0091.

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Review question / Objective: Is acupuncture a safe and effective therapy for constipation associated with Parkinson’s disease? Our aim is to assess the effectiveness and safety of acupuncture for constipation associated with PD and give guidance to future research direction. Condition being studied: Parkinson’s disease (PD) is a prevalent degenerative disease of nervous system characterized mainly by static tremor, bradykinesia, myotonia, postural gait disorders and other non-motor symptoms. According to variations on race, ethnicity, age and sex, the incidence of PD ranges from 8 to 20.5 per 100, 000 individuals annually. One global research shows that there were 6.1 million individuals suffer from PD in 2016 and will be 12 million patients around the world. According to several outcomes of case-control studies, the prevalence of constipation in PD varies from 28% to 61%. Constipation, as a common gastrointestinal disease which refers to the clinical presentation of reduced spontaneous complete bowel movement, dyschezia, feeling of incomplete defecation and outlet obstruction, is demonstrated to antedate the motor symptom and it's severity is related to the progression of PD. Acupuncture has been proved to act on the pathogenesis of constipation associated with PD. The proposed systematic review we're about to present is the first advanced evidence-based medical evidence in this area.
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Eyal, Yoram, and Sheila McCormick. Molecular Mechanisms of Pollen-Pistil Interactions in Interspecific Crossing Barriers in the Tomato Family. United States Department of Agriculture, May 2000. http://dx.doi.org/10.32747/2000.7573076.bard.

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During the evolutionary process of speciation in plants, naturally occurring barriers to reproduction have developed that affect the transfer of genes within and between related species. These barriers can occur at several different levels beginning with pollination-barriers and ending with hybrid-breakdown. The interaction between pollen and pistils presents one of the major barriers to intra- and inter-specific crosses and is the focus of this research project. Our long-term goal in this research proposal was defined to resolve questions on recognition and communication during pollen-pistil interactions in the extended tomato family. In this context, this work was initiated and planned to study the potential involvement of tomato pollen-specific receptor-like kinases (RLK's) in the interaction between pollen and pistils. By special permission from BARD the objectives of this research were extended to include studies on pollen-pistil interactions and pollination barriers in horticultural crops with an emphasis on citrus. Functional characterization of 2 pollen-specific RLK's from tomato was carried out. The data shows that both encode functional kinases that were active as recombinant proteins. One of the kinases was shown to accumulate mainly after pollen germination and to be phosphorylated in-vitro in pollen membranes as well as in-vivo. The presence of style extract resulted in dephosphorylation of the RLK, although no species specificity was observed. This data implies a role for at least one RLK in pollination events following pollen germination. However, a transgenic plant analysis of the RLK's comprising overexpression, dominant-negative and anti-sense constructs failed to provide answers on their role in pollination. While genetic effects on some of the plants were observed in both the Israeli and American labs, no clear functional answers were obtained. An alternative approach to addressing function was pursued by screening for an artificial ligand for the receptor domain using a peptide phage display library. An enriched peptide sequence was obtained and will be used to design a peptide-ligand to be tested for its effect o pollen germination and tube growth. Self-incompatibility (SI) in citrus was studied on 3 varieties of pummelo. SI was observed using fluorescence microscopy in each of the 3 varieties and compatibility relations between varieties was determined. An initial screen for an S-RNase SI mechanism yielded only a cDNA homologous to the group of S-like RNases, suggesting that SI results from an as yet unknown mechanism. 2D gel electrophoresis was applied to compare pollen and style profiles of different compatibility groups. A "polymorphic" protein band from style extracts was observed, isolated and micro-sequenced. Degenerate primers designed based on the peptide sequence date will be used to isolate the relevant genes i order to study their potential involvement in SI. A study on SI in the apple cultivar Top red was initiated. SI was found, as previously shown, to be complete thus requiring a compatible pollinator variety. A new S-RNase allele was discovered fro Top red styles and was found to be highly homologous to pear S-RNases, suggesting that evolution of these genes pre-dated speciation into apples and pears but not to other Rosaceae species. The new allele provides molecular-genetic tools to determine potential pollinators for the variety Top red as well as a tool to break-down SI in this important variety.
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