Relevant bibliographies by topics / Degenerate equation

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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 equation'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Degenerate equation"

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Trudinger, Neil S. "On degenerate fully nonlinear elliptic equations in balls." Bulletin of the Australian Mathematical Society 35, no. 2 (April 1987): 299–307. http://dx.doi.org/10.1017/s0004972700013253.

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We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.
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PERTHAME, BENOÎT, and ALEXANDRE POULAIN. "Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility." European Journal of Applied Mathematics 32, no. 1 (March 24, 2020): 89–112. http://dx.doi.org/10.1017/s0956792520000054.

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The degenerate Cahn–Hilliard equation is a standard model to describe living tissues. It takes into account cell populations undergoing short-range attraction and long-range repulsion effects. In this framework, we consider the usual Cahn–Hilliard equation with a singular single-well potential and degenerate mobility. These degeneracy and singularity induce numerous difficulties, in particular for its numerical simulation. To overcome these issues, we propose a relaxation system formed of two second-order equations which can be solved with standard packages. This system is endowed with an energy and an entropy structure compatible with the limiting equation. Here, we study the theoretical properties of this system: global existence and convergence of the relaxed system to the degenerate Cahn–Hilliard equation. We also study the long-time asymptotics which interest relies on the numerous possible steady states with given mass.
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Agosti, A. "Error analysis of a finite element approximation of a degenerate Cahn-Hilliard equation." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (May 2018): 827–67. http://dx.doi.org/10.1051/m2an/2018018.

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This work considers a Cahn-Hilliard type equation with degenerate mobility and single-well potential of Lennard-Jones type, motivated by increasing interest in diffuse interface modelling of solid tumors. The degeneracy set of the mobility and the singularity set of the potential do not coincide, and the zero of the potential is an unstable equilibrium configuration. This feature introduces a nontrivial difference with respect to the Cahn-Hilliard equation analyzed in the literature. In particular, the singularities of the potential do not compensate the degeneracy of the mobility by constraining the solution to be strictly separated from the degeneracy values. The error analysis of a well posed continuous finite element approximation of the problem, where the positivity of the solution is enforced through a discrete variational inequality, is developed. Whilst in previous works the error analysis of suitable finite element approximations has been studied for second order degenerate and fourth order non degenerate parabolic equations, in this work the a priori estimates of the error between the discrete solution and the weak solution to which it converges are obtained for a degenerate fourth order parabolic equation. The theoretical error estimates obtained in the present case state that the norms of the approximation errors, calculated on the support of the solution in the proper functional spaces, are bounded by power laws of the discretization parameters with exponent 1/2, while in the case of the classical Cahn-Hilliard equation with constant mobility the exponent is 1. The estimates are finally succesfully validated by simulation results in one and two space dimensions.
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Igisinov, S. Zh, L. D. Zhumaliyeva, A. O. Suleimbekova, and Ye N. Bayandiyev. "Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 107, no. 3 (September 30, 2022): 51–58. http://dx.doi.org/10.31489/2022m3/51-58.

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In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure the existence and uniqueness of the solution. The existence, uniqueness, and smoothness of a solution are proved, and estimates are found for singular numbers (s-numbers) and eigenvalues of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration.
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Nazarova, K. "ON ONE METHOD FOR OBTAINING UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR AN INTEGRO-DIFFERENTIAL EQUATION." Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy), no. 1 (March 15, 2022): 42–54. http://dx.doi.org/10.47526/2022-2/2524-0080.04.

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The modified method of parametrization is used to study a linear Fredholm integro-differential equation with a degenerate kernel. Using the fundamental matrix, the conditions are established for the existence of a solution to the special Cauchy problem for the Fredholm integro-differential equation with a degenerate kernel. A system of linear algebraic equations is constructed with respect to the introduced additional parameters. Conditions for the unique solvability of a linear boundary value problem for the Fredholm integro-differential equation with a degenerate kernel are obtained.
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Christodoulou, Dimitris M., Eric Kehoe, and Qutaibeh D. Katatbeh. "Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations." Axioms 10, no. 2 (May 19, 2021): 94. http://dx.doi.org/10.3390/axioms10020094.

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For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known to possess analytic solutions, otherwise their properties and the properties of their solutions are de facto known as they are comparable to those already deduced for the fundamental equation. We analyze several particular cases of new families related to some of the famous differential equations applied to physical problems, and the degenerate eigenstates of the radial Schrödinger equation for the hydrogen atom in N dimensions.
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Koilyshov, U. K., K. A. Beisenbaeva, and S. D. Zhapparova. "A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 107, no. 3 (September 30, 2022): 59–69. http://dx.doi.org/10.31489/2022m3/59-69.

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Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors. Conjugation problems for time-degenerate equations of the parabolic type with discontinuous coefficients are practically not studied. In this work, in an n-dimensional space, a conjugation problem is considered for a heat equation with discontinuous coefficients which degenerates at the initial moment of time. A fundamental solution to the set problem has been constructed and estimates of its derivatives have been found. With the help of these estimates, in the Sobolev classes, the estimate of the solution to the set problem was obtained.
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Gutlyanskiĭ, V., O. Martio, T. Sugawa, and M. Vuorinen. "On the degenerate Beltrami equation." Transactions of the American Mathematical Society 357, no. 3 (October 19, 2004): 875–900. http://dx.doi.org/10.1090/s0002-9947-04-03708-0.

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Henriques, Eurica, and Vincenzo Vespri. "On the double degenerate equation." Nonlinear Analysis: Theory, Methods & Applications 75, no. 4 (March 2012): 2304–25. http://dx.doi.org/10.1016/j.na.2011.10.030.

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Rubinstein, Yanir A., and Jake P. Solomon. "The degenerate special Lagrangian equation." Advances in Mathematics 310 (April 2017): 889–939. http://dx.doi.org/10.1016/j.aim.2017.02.008.

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Dissertations / Theses on the topic "Degenerate equation"

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Tepoyan, L. "The mixed problem for a degenerate operator equation." Universität Potsdam, 2008. http://opus.kobv.de/ubp/volltexte/2009/3033/.

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We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.
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Brinkschulte, Judith. "The Cauchy-Riemann equation with support conditions in domains with Levi degenerate boundaries." [S.l.] : [s.n.], 2002. http://dochost.rz.hu-berlin.de/dissertationen/brinkschulte-judith-2002-04-19.

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Picard, Sebastien. "A priori estimates of the degenerate Monge-Ampère equation on compact Kähler manifolds." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119756.

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The regularity theory of the degenerate complex Monge-Ampère equation is studied. First, the equation is considered on a compact Kahler manifold without boundary. Accordingly, some background information on Kahler geometry is presented. Given a solution of the degenerate complex Monge-Ampère equation, it is shown that its oscillation and gradient can be bounded. The Laplacian of the solution is also estimated. There is a slight improvement from the literature on the conditions required in order to obtain the estimate on the Laplacian of the solution, however the estimates developed only hold in the case of manifolds with non-negative bisectional curvature. As an application, a Dirichlet problem in complex space is considered. The obtained estimates are used to show existence and uniqueness of pluri-subharmonic solutions to the degenerate complex Monge-Ampere equation in a domain in complex space.
La question de la régularité des solutions de l'équation complexe Monge-Ampère dégénérée est étudiée. Premièrement, l'équation est considérée sur une variété compacte Kahler sans frontière. Une revue des concepts clés de la géométrie Kahler est présentée. Étant donné une solution de l'équation complexe Monge-Ampère dégénérée, il est démontré que la différence entre la borne supérieure et la borne inférieure de la solution est sous contrôle, et ainsi pour le gradient de la solution. Le Laplacien de la solution est également bornée. Cette borne du Laplacien est une amélioration de ce qui a été établi dans la littérature jusqu'à présent, mais par contre, l'argument tient seulement sous la condition que la variété a une courbure non-négative. Les résultats sont appliqués à un problème de Dirichlet dans l'espace complexe. L'existence et l'unicité d'une solution pluri-subharmonique de l'équation complexe Monge-Ampère dégénérée dans un domaine contenu dans l'espace complexe est démontré.
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Brinkschulte, Judith. "The Cauchy-Riemann equation with support conditions on domains with Levi-degenerate boundaries." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14734.

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In einem ersten Teil betrachten wir ein relativ kompaktes Gebiet Omega einer n-dimensionalen Kähler-Mannigfaltigkeit, mit Lipschitz-Rand, welches eine gewisse "log delta"-Pseudokonvexität besitzt. Wir zeigen, dass die Cauchy-Riemann Gleichung mit exaktem Träger in Omega für alle Bigrade (p,q) mit 0< q< n-1 eine Lösung besitzt. Ausserdem ist das Bild des Cauchy-Riemann Operators auf glatten (p,n-1)-Formen mit exaktem Träger in Omega abgeschlossen. Wir geben Anwendungen für die Lösbarkeit der tangentialen Cauchy-Riemann Gleichungen für glatte Formen und Ströme auf Rändern von schwach pseudokonvexen Gebieten Steinscher Mannigfaltigkeiten und für die Lösbarkeit der tangentialen Cauchy-Riemann Gleichungen für Ströme auf Levi-flachen CR Mannigfaltigkeiten beliebiger Kodimension. In einem zweiten Teil untersuchen wir die Cauchy-Riemann Gleichung mit Randbedingung Null entlang einer Hyperfläche mit konstanter Signatur. Wir geben Anwendungen für die Lösbarkeit der tangentialen Cauchy-Riemann Gleichung für glatte Formen mit kompaktem Träger und für Ströme auf der Hyperfläche. Wir zeigen auch, dass das Hartogs-Phänomen in schwach 2-konvex-konkaven Hyperflächen mit konstanter Signatur Steinscher Mannigfaltigkeiten gilt.
In a first part, we consider a domain Omega with Lipschitz boundary, which is relatively compact in an n-dimensional Kaehler manifold and satisfies some "log delta-pseudoconvexity" condition. We show that the Cauchy-Riemann equation with exact support in Omega admits a solution in bidegrees (p,q), 1 < q < n. Moreover, the range of the Cauchy-Riemann operator acting on smooth (p,n-1)-forms with exact support in Omega is closed. Applications are given to the solvability of the tangential Cauchy-Riemann equations for smooth forms and currents for all intermediate bidegrees on boundaries of weakly pseudoconvex domains in Stein manifolds and to the solvability of the tangential Cauchy-Riemann equations for currents on Levi-flat CR manifolds of arbitrary codimension. In a second part, we study the Cauchy-Riemann equation with zero Cauchy data along a hypersurface with constant signature. Applications to the solvability of the tangential Cauchy-Riemann equations for smooth forms with compact support and currents on the hypersurface are given. We also prove that the Hartogs phenomenon holds in weakly 2-convex-concave hypersurfaces with constant signature of Stein manifolds.
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Watling, K. D. "Formulae for solutions to (possibly degenerate) diffusion equations exhibiting semi-classical and small time asymptotics." Thesis, University of Warwick, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380277.

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ROCCHETTI, DARIO. "Generation of analytic semigroups for a class of degenerate elliptic operators." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/749.

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Questa tesi è suddivisa in due capitoli. Nel primo si da un risultato di buona positura per una classe di problemi parabolici degeneri. I risultati ottenuti, validi in dimensione 2, garantiscono che le soluzioni di tali problemi supportano l'integrazione per parti. Nel secondo capitolo, si studia la controllabilità allo zero per una classe di operatori parabolici degeneri in forma non-divergenza. In particolare, i coefficienti del termine del secondo ordine possono degenerare al bordo del dominio spaziale. A questo scopo si giunge previo una disuguaglianza di osservabilità per il problema aggiunto usando opportune stime di Carleman.
This thesis is composed by two chapters. The first one is devoted to the generation of analytic semigroups in the L^2 topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimension, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type estimates for degenerate parabolic operators. In the second chapter we give null controllability results for some degenerate parabolic equations in non divergence form with a drift term in one space dimension. In particular, the coefficient of the second order term may degenerate at the extreme points of the space domain. For this purpose, we obtain an observability inequality for the adjoint problem using suitable Carleman estimates.
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Rao, Arvind Satya. "Weak solutions to a Monge-Ampère type equation on Kähler surfaces." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/582.

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In the context of moment maps and diffeomorphisms of Kähler manifolds, Donaldson introduced a fully nonlinear Monge-Ampère type equation. Among the conjectures he made about this equation is that the existence of solutions is equivalent to a positivity condition on the initial data. Weinkove later affirmed Donaldson's conjecture using a gradient flow for the equation in the space of Kähler potentials of the initial data. The topic of this thesis is the case when the initial data is merely semipositive and the domain is a closed Kähler surface. Regularity techniques for degenerate Monge-Ampère equations, specifically those coming from pluripotential theory, are used to prove the existence of a bounded, unique, weak solution. With the aid of a Nakai criterion, due to Lamari and Buchdahl, it is shown that this solution is smooth away from some curves of negative self-intersection.
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Boiger, Wolfgang Josef. "Stabilised finite element approximation for degenerate convex minimisation problems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16790.

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Infimalfolgen nichtkonvexer Variationsprobleme haben aufgrund feiner Oszillationen häufig keinen starken Grenzwert in Sobolevräumen. Diese Oszillationen haben eine physikalische Bedeutung; Finite-Element-Approximationen können sie jedoch im Allgemeinen nicht auflösen. Relaxationsmethoden ersetzen die nichtkonvexe Energie durch ihre (semi)konvexe Hülle. Das entstehende makroskopische Modell ist degeneriert: es ist nicht strikt konvex und hat eventuell mehrere Minimalstellen. Die fehlende Kontrolle der primalen Variablen führt zu Schwierigkeiten bei der a priori und a posteriori Fehlerschätzung, wie der Zuverlässigkeits- Effizienz-Lücke und fehlender starker Konvergenz. Zur Überwindung dieser Schwierigkeiten erweitern Stabilisierungstechniken die relaxierte Energie um einen diskreten, positiv definiten Term. Bartels et al. (IFB, 2004) wenden Stabilisierung auf zweidimensionale Probleme an und beweisen dabei starke Konvergenz der Gradienten. Dieses Ergebnis ist auf glatte Lösungen und quasi-uniforme Netze beschränkt, was adaptive Netzverfeinerungen ausschließt. Die vorliegende Arbeit behandelt einen modifizierten Stabilisierungsterm und beweist auf unstrukturierten Netzen sowohl Konvergenz der Spannungstensoren, als auch starke Konvergenz der Gradienten für glatte Lösungen. Ferner wird der sogenannte Fluss-Fehlerschätzer hergeleitet und dessen Zuverlässigkeit und Effizienz gezeigt. Für Interface-Probleme mit stückweise glatter Lösung wird eine Verfeinerung des Fehlerschätzers entwickelt, die den Fehler der primalen Variablen und ihres Gradienten beschränkt und so starke Konvergenz der Gradienten sichert. Der verfeinerte Fehlerschätzer konvergiert schneller als der Fluss- Fehlerschätzer, und verringert so die Zuverlässigkeits-Effizienz-Lücke. Numerische Experimente mit fünf Benchmark-Tests der Mikrostruktursimulation und Topologieoptimierung ergänzen und bestätigen die theoretischen Ergebnisse.
Infimising sequences of nonconvex variational problems often do not converge strongly in Sobolev spaces due to fine oscillations. These oscillations are physically meaningful; finite element approximations, however, fail to resolve them in general. Relaxation methods replace the nonconvex energy with its (semi)convex hull. This leads to a macroscopic model which is degenerate in the sense that it is not strictly convex and possibly admits multiple minimisers. The lack of control on the primal variable leads to difficulties in the a priori and a posteriori finite element error analysis, such as the reliability-efficiency gap and no strong convergence. To overcome these difficulties, stabilisation techniques add a discrete positive definite term to the relaxed energy. Bartels et al. (IFB, 2004) apply stabilisation to two-dimensional problems and thereby prove strong convergence of gradients. This result is restricted to smooth solutions and quasi-uniform meshes, which prohibit adaptive mesh refinements. This thesis concerns a modified stabilisation term and proves convergence of the stress and, for smooth solutions, strong convergence of gradients, even on unstructured meshes. Furthermore, the thesis derives the so-called flux error estimator and proves its reliability and efficiency. For interface problems with piecewise smooth solutions, a refined version of this error estimator is developed, which provides control of the error of the primal variable and its gradient and thus yields strong convergence of gradients. The refined error estimator converges faster than the flux error estimator and therefore narrows the reliability-efficiency gap. Numerical experiments with five benchmark examples from computational microstructure and topology optimisation complement and confirm the theoretical results.
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Čakaitė, Inga. "Dalinių išvestinių sistemos su kvazireguliariuoju išsigimimu sprendimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2006. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060609_122917-49917.

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The system of the four partial fluxions of the primary row of differential equations the row of which dwindles at the points of plane has been analysed. The systems of the expressions of families of the detached solutions have been derived by converging degree rows at the environment of malformation rows through the technique of summation of degree rows. The solutions at the malformation points are particular for having degree particularities. Still, the particularities depend on the other to variables, in conformity to which there are no system malformation weigh. The effect is not evident in the analytical theory of malformed vulgar differential equation.
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Mumcu, Gokhan. "EM Characterization of Magnetic Photonic / Degenerate Band Edge Crystals and Related Antenna Realizations." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1221860344.

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Books on the topic "Degenerate equation"

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Wakako, Hideaki. Exact WKB analysis for the degenerate third Painleve equation of type (Ds). Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2007.

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Levendorskii, Serge. Degenerate Elliptic Equations. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6.

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DiBenedetto, Emmanuele. Degenerate Parabolic Equations. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0895-2.

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Levendorskiĭ, Serge. Degenerate elliptic equations. Dordrecht: Kluwer, 1993.

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DiBenedetto, Emmanuele. Degenerate parabolic equations. New York: Springer-Verlag, 1993.

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Favini, Angelo, and Gabriela Marinoschi. Degenerate Nonlinear Diffusion Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28285-0.

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Favini, Angelo. Degenerate Nonlinear Diffusion Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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A, Dzhuraev. Degenerate and other problems. Harlow, Essex, England: Longman Scientific and Technical, 1992.

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Ahmed, Zeriahi, ed. Degenerate complex Monge--Ampère equations. Zürich, Switzerland: European Mathematical Society Publishing House, 2017.

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Favini, A. Degenerate differential equations in Banach spaces. New York: Marcel Dekker, 1999.

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Book chapters on the topic "Degenerate equation"

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Arrieta, José M., Rosa Pardo, and Aníbal Rodríguez-Bernal. "A Degenerate Parabolic Logistic Equation." In Advances in Differential Equations and Applications, 3–11. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06953-1_1.

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Galaktionov, Victor A., and Sergey A. Posashkov. "On Some Monotonicity in Time Properties for a Quasilinear Parabolic Equation with Source." In Degenerate Diffusions, 77–93. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0885-3_5.

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Efendiev, Messoud. "Porous medium equation in homogeneous media: Long-time dynamics." In Attractors for Degenerate Parabolic Type Equations, 67–87. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/04.

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Efendiev, Messoud. "Porous medium equation in heterogeneous media: Long-time dynamics." In Attractors for Degenerate Parabolic Type Equations, 89–99. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/05.

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Rodrigues, José Francisco, and Hugo Tavares. "Increasing Powers in a Degenerate Parabolic Logistic Equation." In Partial Differential Equations: Theory, Control and Approximation, 379–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-41401-5_15.

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Krejčí, Pavel. "Boundedness of Solutions to a Degenerate Diffusion Equation." In Springer INdAM Series, 305–26. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64489-9_12.

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Slathia, Geetika, Rajneet Kaur, Kuldeep Singh, and Nareshpal Singh Saini. "Forced KdV Equation in Degenerate Relativistic Quantum Plasma." In Nonlinear Dynamics and Applications, 15–24. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99792-2_2.

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Fragnelli, Genni, and Dimitri Mugnai. "The Case of an Interior Degenerate/Singular Parabolic Equation." In SpringerBriefs in Mathematics, 85–97. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69349-7_5.

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Fragnelli, Genni, and Dimitri Mugnai. "The Case of a Boundary Degenerate/Singular Parabolic Equation." In SpringerBriefs in Mathematics, 71–84. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69349-7_4.

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Ricciotti, Diego. "$$C^\infty $$ C ∞ Regularity for the Non-degenerate Equation." In SpringerBriefs in Mathematics, 43–61. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23790-9_4.

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Conference papers on the topic "Degenerate equation"

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Goncerzewicz, Jan. "On the initial-boundary value problems for a degenerate parabolic equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-13.

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BRESCH, DIDIER, and PIERRE-EMMANUEL JABIN. "QUANTITATIVE ESTIMATES FOR ADVECTIVE EQUATION WITH DEGENERATE ANELASTIC CONSTRAINT." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0134.

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Butuzov, Valentin Fedorovich. "Singularly perturbed ODEs with multiple roots of the degenerate equation." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Moscow: Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc22964.

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"Solvability of the quasilinear degenerate equation with Dzhrbashyan — Nersesyan derivative." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.84.

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Шуклина, Анна, and Марина Плеханова. "Mixed control of solutions to a degenerate nonlinear fractional equation." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh2t-2021-10-06.47.

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Yuldashev, Tursun K. "On a Volterra type fractional integro-differential equation with degenerate kernel." In INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0057135.

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Nikolov, Aleksey, and Nedyu Popivanov. "Singular solutions to Protter's problem for (3+1)-D degenerate wave equation." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766790.

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Marinoschi, Gabriela. "Identification of a singular coefficient in a parabolic degenerate equation with transport." In ALEXANDRU MYLLER MATHEMATICAL SEMINAR CENTENNIAL CONFERENCE. AIP, 2011. http://dx.doi.org/10.1063/1.3546085.

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Zhang, Wei, Feng-Xia Wang, and Hong-Bo Wen. "Studies on Codimension-3 Degenerate Bifurcations of the Flexible Beam." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21586.

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Abstract:
Abstract We present the analysis of codimension-3 degenerate bifurcations of a simply supported flexible beam subjected to harmonic axial excitation. The equation of motion with quintic nonlinear terms and the parametrical excitation for the simply supported flexible beam is derived. The main attention is focused on the dynamical properties of the global bifurcations including homoclinic bifurcations. With the aid of normal form theory, the explicit expressions of normal form associated with a double zero eigenvalues and Z2-symmetry for the averaged equations are obtained. Based on the normal form, it has been shown that a simply supported flexible beam subjected to the harmonic axial excitation can exhibit homoclinic bifurcations, multiple limit cycles, and jumping phenomena in amplitude modulated oscillations. Numerical simulations are also given to verify the good analytical predictions.
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Nikolov, Aleksey, and Nedyu Popivanov. "Riemann-Hadamard method for solving a (2+1)-D problem for degenerate hyperbolic equation." In 41ST INTERNATIONAL CONFERENCE “APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS” AMEE ’15. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4936708.

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Reports on the topic "Degenerate equation"

1

Fujisaki, Masatoshi. Normed Bellman Equation with Degenerate Diffusion Coefficients and Its Application to Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada190319.

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Nohel, John A. A Class of One-Dimensional Degenerate Parabolic Equations. Fort Belvoir, VA: Defense Technical Information Center, July 1985. http://dx.doi.org/10.21236/ada160962.

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Gupta, V., B. H. J. McKellar, and D. D. Wu. The degeneracy of the free Dirac equation. Office of Scientific and Technical Information (OSTI), August 1991. http://dx.doi.org/10.2172/6105369.

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