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Добірка наукової літератури з теми "Nonlocal equations in time"

Автор: Grafiati
Опубліковано: 15 березня 2025

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Статті в журналах з теми "Nonlocal equations in time"

1

Dong, Hongjie, Chulan Zeng, and Qi S. Zhang. "Time Analyticity for Nonlocal Parabolic Equations." SIAM Journal on Mathematical Analysis 55, no. 3 (June 7, 2023): 1883–915. http://dx.doi.org/10.1137/22m1490740.

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2

Ding, Xiao-Li, and Juan J. Nieto. "Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms." Fractional Calculus and Applied Analysis 21, no. 2 (April 25, 2018): 312–35. http://dx.doi.org/10.1515/fca-2018-0019.

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AbstractIn this paper, we consider the analytical solutions of multi-term time-space fractional partial differential equations with nonlocal damping terms for general mixed Robin boundary conditions on a finite domain. Firstly, method of reduction to integral equations is used to obtain the analytical solutions of multi-term time fractional differential equations with integral terms. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the multi-term time-space fractional partial differential equations with nonlocal damping terms to the multi-term time fractional differential equations with integral terms. By applying the obtained analytical solutions to the resulting multi-term time fractional differential equations with integral terms, the desired analytical solutions of the multi-term time-space fractional partial differential equations with nonlocal damping terms are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.
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3

Ablowitz, Mark J., and Ziad H. Musslimani. "Integrable space-time shifted nonlocal nonlinear equations." Physics Letters A 409 (September 2021): 127516. http://dx.doi.org/10.1016/j.physleta.2021.127516.

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4

Morawetz, Klaus, Pavel Lipavský, and Václav Špička. "Retarded versus Time-Nonlocal Quantum Kinetic Equations." Annals of Physics 294, no. 2 (December 2001): 135–64. http://dx.doi.org/10.1006/aphy.2001.6197.

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5

Lv, Cong, Deqin Qiu, and Q. P. Liu. "Riemann–Hilbert approach to two-component modified short-pulse system and its nonlocal reductions." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 9 (September 2022): 093120. http://dx.doi.org/10.1063/5.0088293.

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In this paper, a Riemann–Hilbert approach to a two-component modified short-pulse (mSP) system on the line with zero boundary conditions is developed. A parametric representation of the solution to the related Cauchy problem is obtained. Four nonlocal integrable reductions, namely, the real reverse space-time nonlocal focusing and defocusing mSP equations and the complex reverse space-time nonlocal focusing and defocusing mSP equations, are studied in detail. For each case, soliton solutions are presented, and, unlike their local counterparts, the nonlocal equations exhibit certain novel properties induced by the impact of nonlocality.
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6

Cichoń, Mieczysław, Bianca Satco, and Aneta Sikorska-Nowak. "Impulsive nonlocal differential equations through differential equations on time scales." Applied Mathematics and Computation 218, no. 6 (November 2011): 2449–58. http://dx.doi.org/10.1016/j.amc.2011.07.057.

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7

Ludu, Andrei. "Nonlocal Symmetries for Time-Dependent Order Differential Equations." Symmetry 10, no. 12 (December 19, 2018): 771. http://dx.doi.org/10.3390/sym10120771.

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A new type of ordinary differential equation is introduced and discussed: time-dependent order ordinary differential equations. These equations are solved via fractional calculus by transforming them into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equation represent deformations of the solutions of the classical (integer order) differential equations, mapping them into one-another as limiting cases. This equation can also move, remove or generate singularities without involving variable coefficients. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers is observed.
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8

Feng, Wei, and Song-Lin Zhao. "Soliton solutions to the nonlocal non-isospectral nonlinear Schrödinger equation." International Journal of Modern Physics B 34, no. 25 (September 9, 2020): 2050219. http://dx.doi.org/10.1142/s0217979220502197.

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In this paper we study the nonlocal reductions for the non-isospectral Ablowitz-Kaup-Newell-Segur equation. By imposing the real and complex nonlocal reductions on the non-isospectral Ablowitz-Kaup-Newell-Segur equation, we derive two types of nonlocal non-isospectral nonlinear Schrödinger equations, in which one is real nonlocal non-isospectral nonlinear Schrödinger equation and the other is complex nonlocal non-isospectral nonlinear Schrödinger equation. Of both of these two equations, there are the reverse time nonlocal type and the reverse space nonlocal type. Soliton solutions in terms of double Wronskian to the reduced equations are obtained by imposing constraint conditions on the double Wronskian solutions of the non-isospectral Ablowitz-Kaup-Newell-Segur equation. Dynamics of the one-soliton solutions are analyzed and illustrated by asymptotic analysis.
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9

Ashurov, Ravshan, and Yusuf Fayziev. "On the Nonlocal Problems in Time for Time-Fractional Subdiffusion Equations." Fractal and Fractional 6, no. 1 (January 12, 2022): 41. http://dx.doi.org/10.3390/fractalfract6010041.

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The nonlocal boundary value problem, dtρu(t)+Au(t)=f(t) (0<ρ<1, 0<t≤T), u(ξ)=αu(0)+φ (α is a constant and 0<ξ≤T), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operator A, is considered. The operator dt on the left hand side of the equation expresses either the Caputo derivative or the Riemann–Liouville derivative; naturally, in the case of the Riemann–Liouville derivatives, the nonlocal boundary condition should be slightly changed. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence of a solution to problems is investigated. Inequalities of coercivity type are obtained and it is shown that these inequalities differ depending on the considered type of fractional derivatives. The inverse problems of determining the right-hand side of the equation and the function φ in the boundary conditions are investigated.
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10

Ma, Wen-Xiu. "Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)". Proceedings of the American Mathematical Society, Series B 9, № 1 (14 січня 2022): 1–11. http://dx.doi.org/10.1090/bproc/116.

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We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) . The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal reverse-space, reverse-time and reverse-spacetime nonlinear Schrödinger equations associated with so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) .
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Більше джерел

Дисертації з теми "Nonlocal equations in time"

1

Hariz, Belgacem Khader. "Higher-order Embedding Formalism, Noether’s Theorem on Time Scales and Eringen’s Nonlocal Elastica." Electronic Thesis or Diss., Pau, 2022. https://theses.hal.science/tel-03981833.

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En mathématiques, le calcul des variations est un ensemble de méthodes permettant la détermination de solutions à des problèmes d'optimisation des quantités traduites en termes de fonctionnelle. De nombreuses applications existent, notamment dans la recherche de courbes ou de surfaces minimales. Les systèmes dynamiques considérés sont de natures diverses (équations différentielles, intégrales ou stochastiques) et modélisent des problèmes d'origines multiples : aérospatiale, automobile, biologie, économie, médecine, etc. Le théorème de Noether présente un fort intérêt puisqu'il propose une loi de conservation explicite (traduisant souvent une quantité physique comme l'énergie totale ou le moment angulaire en mécanique classique) qui permet de réduire ou d'intégrer l'équation différentielle associée par quadrature. L'objectif de ma thèse contient de nombreux thèmes, dans le premier but nous allons : *) donner le théorème de Noether discret dans le cadre ”time scale” (Le formalisme lagrangien et hamiltonien). Le passage de la nature discrète à la nature continue de la structure la morphologie est d'un intérêt primordial en physique pour comprendre comment la microstructure peut influencer les propriétés macroscopiques du matériau à plus grande échelle. Ce passage peut être modélisé par un système discret appelé 'Hencky's chain' et l'équation du mouvement est donnée par des équations aux différences non linéaires et cette équation ne possède pas de Lagrangien. Le deuxième but nous allons : *) donner les structures lagrangienne, hamiltonienne via le facteur intégrant et trouver la solution analytique de l'équation non locale au sens d'Eringen (nonlocalité différentielle d'Eringen, 1983). Le troisième but nous allons : *) étudier l'existence des formulations variationnelles via le principe de Brezis Ekeland-Nayroles (Gery de Saxce) - application sur la formulation 4D développée par E. Rouhaud pour l'étude des déformations des matériaux *) développer des schémas numériques qui respectent certaines particularités. En particulier, un schéma permettent de mettre en œuvre la théorie 4D développée par E. Rouhaud. *) applications numériques et théoriques sur le problème des déformations des matériaux
The aim of this thesis is to deal with the connection between continuous and discrete versions of a given object. This connection can be studied in two different directions: one going from a continuous setting to a discrete analogue, and in a symmetric way, from a discrete setting to a continuous one. The first procedure is typically used in numerical analysis in order to construct numerical integrators and the second one is typical of continuous modeling for the study of micro-structured materials.In this manuscript, we focus our attention on three distinct problems. In the first part, we propose a general framework precising different ways to derive a discrete version of a differential equation called discrete embedding formalism.More precisely, we exhibit three main discrete associate: the differential, integral or variational structure in both classical and high-order approximations.The second part focuses on the preservation of symmetries for discrete versions of Lagrangian and Hamiltonian systems, i.e., the discrete analogue of Noether's theorem.Finally, the third part applies these results in mechanics, i.e., the problem studied by N. Challamel, Kocsis and Wang called Eringen's nonlocal elastica equation which can beobtained by the continualization method. Precisely, we construct a discrete version of Eringen's nonlocal elastica then we study the difference with Challamel's proposal
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2

Figueroa, Iglesias Susely. "Integro-differential models for evolutionary dynamics of populations in time-heterogeneous environments." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30098.

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Cette thèse porte sur l'étude qualitative de plusieurs équations paraboliques de type Lotka-Volterra issues de la biologie évolutive et de l'écologie, équations qui prennent en compte un taux de croissance périodique en temps et un phénomène de compétition non locale. Dans une première partie nous étudions d'abord la dynamique des populations phénotypiquement structurées sous l'effet des mutations et de la sélection dans des environnements qui varient périodiquement en temps, puis nous étudions l'impact d'un changement climatique sur ces populations, en considérant que les conditions environnementales varient selon une tendance linéaire, mais de manière oscillatoire. Dans les deux problèmes nous commençons par étudier le comportement en temps long des solutions. Ensuite nous utilisons une approche basée sur les équations de Hamilton-Jacobi pour l'étude asymptotique de ces solutions en temps long lorsque l'effet des mutations est petit. Nous prouvons que lorsque l'effet des mutations disparaît, la densité phénotypique de la population se concentre sur un seul trait (qui varie linéairement avec le temps dans le deuxième modèle), tandis que la taille de la population oscille périodiquement. Pour le modèle de changement climatique nous fournissons également un développement asymptotique de la taille moyenne de la population et de la vitesse critique menant à l'extinction de la population, ce qui est lié à la dérivation d'un développement asymptotique de la valeur propre de Floquet en fonction du taux de diffusion. Dans la deuxième partie, nous étudions quelques exemples particuliers de taux de croissance en donnant des solutions explicites et semi-explicites au problème, et nous présentons quelques illustrations numériques pour le modèle périodique. De plus, étant motivés par une expérience biologique, nous comparons deux populations évoluant dans des environnements différents (constants ou périodiques). En outre, nous présentons une comparaison numérique entre les modèles stochastiques et déterministes pour le phénomène de transfert horizontal des gènes. Dans un contexte Hamilton-Jacobi, nous parvenons à reproduire numériquement le sauvetage évolutif d'une petite population que nous observons dans le modèle stochastique
This thesis focuses on the qualitative study of several parabolic equations of the Lotka-Volterra type from evolutionary biology and ecology taking into account a time-periodic growth rate and a non-local competition term. In the initial part we first study the dynamics of phenotypically structured populations under the effect of mutations and selection in environments that vary periodically in time and then the impact of a climate change on such population considering environmental conditions which vary according to a linear trend, but in an oscillatory manner. In both problems we first study the long-time behaviour of the solutions. Then we use an approach based on Hamilton-Jacobi equations to study these long-time solutions asymptotically when the effect of mutations is small. We prove that when the effect of mutations vanishes, the phenotypic density of the population is concentrated on a single trait (which varies linearly over time in the second model), while the population size oscillates periodically. For the climate change model we also provide an asymptotic expansion of the mean population size and of the critical speed leading to the extinction of the population, which is closely related to the derivation of an asymptotic expansion of the Floquet eigenvalue in terms of the diffusion rate. In the second part we study some particular examples of growth rates by providing explicit and semi-explicit solutions to the problem and present some numerical illustrations for the periodic model. In addition, being motivated by a biological experiment, we compare two populations evolved in different environments (constant or periodic). In addition, we present a numerical comparison between stochastic and deterministic models modelling the horizontal gene transfer phenomenon. In a Hamilton-Jacobi context, we are able to numerically reproduce the evolutionary rescue of a small population that we observe in the stochastic model
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3

Belin, Théo. "On the free boundary of a forward-backward parabolic equation." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM040.

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Dans cette thèse, nous nous intéressons à un problème parabolique de type avance-rétrograde ainsi que la frontière libre qui en découle. L'équation modélise un changement de phase dirigé par un problème de Stefan couplé avec un opérateur d'hystérésis non local en temps. Notre étude s'occupe de questions théoriques et numériques soulevées par ce type d'équations non locales en temps, notamment autour de la frontière libre.Premièrement nous établissons une équivalence entre des inégalités d'entropie associées au problème avance-rétrograde et une formulation faible de l'opérateur d'hystérésis. Cette découverte motive la construction d'un schéma numérique de type volumes finis, en dimension quelconque d'espace, dont nous démontrons la convergence vers une solution. La compacité de la suite de solutions approchées repose sur l'inégalité de Hilpert. Des expériences numériques en dimensions 1 et 2 étayent ces résultats et montrent le comportement la frontière libre.Ensuite nous établissons un cadre général de solutions de viscosité pour des équations de propagation de front qui sont non locales en espace et en temps. Elles peuvent notamment inclure un couplage avec une équation d'évolution interne. Un théorème de comparaison strict ainsi qu'un théorème d'existence issu de la méthode de Perron sont démontrés. Le problème de Stefan ainsi que quelques variations de ce problème rentrent dans ce cadre général.Enfin, motivés par l'étude des équations paraboliques en domaines variables en temps apparaissant dans les couplages des équations de front, nous démontrons de nouveaux résultats de régularité maximale dans les espaces de Lebesgues. Un intérêt particulier est porté sur l'estimation précise de la constante de régularité pour les opérateurs non-autonomes et relativement continus. Ces résultats sont à l'origine de nouvelles hypothèses de croissance garantissant l'existence de solutions fortes et globales à des problèmes quasi-linéaires abstraits sur un interval en temps borné
In this thesis, we focus on a forward-backward parabolic problem and the free boundary arising from it. The equation models a phase change driven by a Stefan problem coupled with a time nonlocal hysteresis operator. Our study deals with some theoretical and numerical aspects raised by this type of time nonlocal equation, in particular regarding the free boundary.First, we establish an equivalence between entropy inequalities associated with the problem and a weak formulation of the hysteresis operator. This discovery motivates the construction of a finite-volume numerical scheme whose convergence to a solution is shown. The compactness of the sequence of approximate solutions is based on Hilpert's inequality. Numerical experiments in dimensions 1 and 2 support these results and illustrate the behaviour of the free boundary.Next we establish a general framework of viscosity solutions for front propagation problems which are nonlocl in space and time. They may include a coupling with a bulk evolution equation. A strict comparison theorem and an existence theorem derived from Perron's method are proved. The Stefan problem and some variations of it fall within this general framework.Finally, motivated by the study of parabolic equations in time-varying domains appearing in couplings of front propagation problems, we prove new results of maximal regularity in Lebesgue spaces. Of particular interest is the precise estimation of the regularity constant for nonautonomous and relatively continuous operators. These results lead to new growth conditions guaranteeing the existence of strong global solutions to abstract quasi-linear problems on a bounded time interval
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4

Freitas, Pedro S. C. de. "Some problems in nonlocal reaction-diffusion equations." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/1401.

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5

Begg, Ronald Evan. "Cell-population growth modelling and nonlocal differential equations." Thesis, University of Canterbury. Mathematics and Statistics, 2007. http://hdl.handle.net/10092/1165.

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Aspects of the asymptotic behaviour of cell-growth models described by partial differential equations, and systems of partial differential equations, are considered. The models considered describe the evolution of the size-distribution or age-distribution of a population of cells undergoing growth and division. First, the relationship between the behaviour, with and without dispersion, of a single-compartment size-distribution model of cell-growth with fixed-size cell division (where cells can only divide at a single, critical size) is considered. In this model dispersion accounts for stochastic variation in the growth process of each individual cell. Existence, uniqueness and the asymptotic stability of the solution is shown for a size-distribution model of cell-growth with dispersion and fixed-size cell division. The conditions for the analysis to hold for a more general class of division behaviours are also discussed. A class of nonlocal ordinary differential equations is studied, which contains as a subset the nonlocal ordinary differential equations describing the steady size-distributions of a single-compartment model of cell-growth. Existence of solutions to these equations is found to be implied by the existence of 'upper' and 'lower' solutions, which also provide bounds for the solution. A multi-compartment, age-distribution model of cell-growth is studied, which describes the evolution of the age-distribution of cells in different phases of cell-growth. The stability of the model when periodic solutions exist is examined. Sufficient conditions are given for the existence of stable steady age-distributions, as well as for stable periodic solutions. Finally, a multi-compartment age-size distribution model of cell-growth is studied, which describes the evolution of the age-size distribution of cells in different phases of cell-growth. Sufficient conditions are given for the existence of steady age-size distributions. An outline of the analysis required to prove stability of the steady age-size distributions of the model is also given. The analysis is based on ideas introduced in the previous chapters.
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6

Wang, Ying. "Contributions to local and nonlocal elliptic differential equations." Tesis, Universidad de Chile, 2015. http://repositorio.uchile.cl/handle/2250/134657.

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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática
Esta tesis doctoral está dividida en cuatro partes. La primera parte está dedicada al estudio de la simetría radial y las propiedades de monotonicidad de soluciones positivas de ecuaciones elípticas fraccionarias en la bola unitaria o en todo el espacio, usando el método de planos móviles. En la segunda parte, se consideran propiedades de decaimiento y simetría de las soluciones positivas para ecuaciones integro-diferenciales en todo el espacio. Estudiamos el decaimiento, construyendo super y subsoluciones apropiadas y usamos el método de los planos móviles para probar las propiedades de simetría. La tercera parte es investigar la existencia y unicidad de soluciones débiles de la ecuación del calor fraccionaria, involucrando medidas de Radon. Más aún, analizamos el comportamiento asintótico de la solución débil cuando la medida de Radon es la masa de Dirac. En la cuarta parte, estudiamos la existencia de soluciones a problemas elípticos no lineales que provienen del modelamiento de dispositivos de sistemas micro-electromecánicos en el caso en que la membrana elástica entra en contacto con la placa inferior en la frontera. Mostramos, en este caso, como el decaimiento de la membrana afecta la existencia de soluciones y la tensión pull-in.
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7

Felsinger, Matthieu [Verfasser]. "Parabolic equations associated with symmetric nonlocal operators / Matthieu Felsinger." Bielefeld : Universitätsbibliothek Bielefeld, 2013. http://d-nb.info/1042557322/34.

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8

Wu, Lijiang. "Nonlocal Interaction Equations in Heterogeneous and Non-Convex Environments." Research Showcase @ CMU, 2015. http://repository.cmu.edu/dissertations/474.

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9

Hollender, Julian. "Lévy-Type Processes under Uncertainty and Related Nonlocal Equations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-211795.

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The theoretical study of nonlinear expectations is the focus of attention for applications in a variety of different fields — often with the objective to model systems under incomplete information. Especially in mathematical finance, advances in the theory of sublinear expectations (also referred to as coherent risk measures) lay the theoretical foundation for modern approaches to evaluations under the presence of Knightian uncertainty. In this book, we introduce and study a large class of jump-type processes for sublinear expectations, which can be interpreted as Lévy-type processes under uncertainty in their characteristics. Moreover, we establish an existence and uniqueness theory for related nonlinear, nonlocal Hamilton-Jacobi-Bellman equations with non-dominated jump terms.
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10

Topp, Paredes Erwin. "Some results for nonlocal elliptic and parabolic nonlinear equations." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/129978.

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Анотація:
Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática
\quad Esta tesis est\'a dedicada al estudio de propiedades cualitativas de ecuaciones el\'ipticas degeneradas donde la difusi\'on es puramente no local, y se lleva a cabo en el contexto de la teor\'ia de soluciones viscosas. La primera parte de la tesis trata el estudio de propiedades de compacidad de una familia de \textsl{operadores no locales de orden cero}, es decir, operadores el\'ipticos no locales definidos a trav\'es de una medida finita. Consideramos un familia uni-param\'etrica de operadores de orden cero de la forma \begin \mathcal_\epsilon(u, x) = \int_ [u(x + z) - u(x)]K_\epsilon(z)dz, \end donde, para cada $\epsilon \in (0,1)$, $K_\epsilon \in L^1(\mathbb^N)$ es una funci\'on radialmente sim\'etrica y positiva. Configuramos nuestro problema de manera que $\mathcal_\epsilon$ aproxime el Laplaciano fraccionario cuando $\epsilon \to 0^+$, lo que implica que la norma $L^1$ de $K_\epsilon$ es no acotada a medida que $\epsilon \to 0^+$. Como primer resultado de esta parte obtenemos un m\'odulo de continuidad en espacio-tiempo para la familia de soluciones acotadas de la ecuaci\'on del calor no local en el plano asociada a $\mathcal_\epsilon$ que es independiente de $\epsilon \in (0,1)$. El segundo resultado de esta parte considera un problema de Dirichlet en un dominio acotado $\Omega \subset \mathbb^N$ asociado a $\mathcal_\epsilon$, y concluimos la compacidad de la familia de soluciones acotadas $\_\epsilon$ para estos problemas de Dirichlet encontrando un m\'odulo de continuidad com\'un en $\bar$ para $\_\epsilon$, que es independiente de $\epsilon$. \medskip La segunda parte de la tesis est\'a relacionada con la existencia y unicidad, regularidad y comportamiento a grandes tiempos para ecuaciones no locales con t\'erminos de gradiente dominantes. Comenzamos con la existencia y unicidad de una ecuaci\'on de Hamilton-Jacobi de la forma \begin{equation*} \begin{array}{rll} \lambda u - \mathcal{I}(u) + H(x, Du) & = 0 \quad & \mbox{en} \ \Omega \\ u & = \varphi \quad & \mbox{en} \ \Omega^c, \end{array} \end{equation*} donde el Hamiltoniano $H$ tiene una \textsl{forma de Bellman}. Estructuramos el problema de manera que el operador no local $\mathcal{I}$ es de orden menor que $1$ y por lo tanto puede aparecer una p\'erdida de la condici\'on de borde. En la segunda secci\'on de esta parte, consideramos $H$ coercivo con un crecimiento en el gradiente m\'as fuerte que el orden de la difusi\'on del operador no local. El resultado principal en este caso es la continuidad H\"older para \textsl{subsoluciones} para este problema. Estabilidad de las estimaciones de regularidad cuando $\lambda \to 0$ permiten concluir el comportamiento asint\'otico erg\'odico cuando $t \to \infty$ para el problema parab\'olico asociado en el toro. En esta tarea, principios del m\'aximo fuertes son de importancia mayor en el an\'alisis asint\'otico. Finalmente, adaptamos los resultados obtenidos en las primeras dos secciones de esta parte de la tesis para obtener el comportamiento a grandes tiempos para el problema de Cauchy-Dirichlet asociado a $H$ en las formas Bellman y coercivo. En este caso, la influencia del dato exterior en la ecuaci\'on a trav\'es del t\'ermino no local hace que el problema parab\'olico aproxime al correspondiente problema estacionario cuando $t \to \infty$.
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Книги з теми "Nonlocal equations in time"

1

E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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4

Andreu-Vaillo, Fuensanta. Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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5

Shishmarev, I. A. (Ilʹi͡a︡ Andreevich)., ed. Nonlinear nonlocal equations in the theory of waves. Providence, R.I: American Mathematical Society, 1994.

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6

Naumkin, P. I. Nonlinear nonlocal equations in the theory of waves. Providence, R.I: American Mathematical Society, 1994.

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7

Roquejoffre, Jean-Michel. The Dynamics of Front Propagation in Nonlocal Reaction–Diffusion Equations. Cham: Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-77772-1.

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8

1958-, Biler Piotr, Karch Grzegorz, and Nadzieja Tadeusz 1951-, eds. Nonlocal elliptic and parabolic problems: Proceedings of the conference held at Będlewo , September 12-15, 2003. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2004.

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9

Kamenskiĭ, G. A. Extrema of nonlocal functionals and boundary value problems for functional differential equations. Hauppauge, N.Y: Nova Science Publishers, 2007.

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10

Kubica, Adam, Katarzyna Ryszewska, and Masahiro Yamamoto. Time-Fractional Differential Equations. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-9066-5.

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Частини книг з теми "Nonlocal equations in time"

1

Ablowitz, Mark J., and Ziad H. Musslimani. "Integrable Nonlocal PT Symmetric and Reverse Space-Time Nonlinear Schrödinger Equations." In Springer Tracts in Modern Physics, 493–512. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1247-2_17.

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2

Monvel, Anne Boutet de, Yan Rybalko, and Dmitry Shepelsky. "Focusing Nonlocal Nonlinear Schrödinger Equation with Asymmetric Boundary Conditions: Large-Time Behavior." In Toeplitz Operators and Random Matrices, 193–227. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13851-5_11.

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Chen, Jingkai. "Nonlocal Beam Equations." In Nonlocal Euler–Bernoulli Beam Theories, 5–7. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_2.

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4

Georgiev, Slavi G., and Lubin G. Vulkov. "Recovering the Time-Dependent Volatility and Interest Rate in European Options from Nonlocal Price Measurements by Adjoint Equation Optimization." In Advanced Computing in Industrial Mathematics, 45–55. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20951-2_5.

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5

Heimsoeth, B., and H. Lange. "Nonlocal Nonlinear Schrödinger Equations." In Semigroup Theory and Evolution Equations, 243–57. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9781003419914-17.

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Volpert, Vitaly. "Nonlocal Reaction-diffusion Equations." In Elliptic Partial Differential Equations, 521–626. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0813-2_9.

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7

Meher, Ramakanta. "Nonlocal Existence Theorem." In Textbook on Ordinary Differential Equations, 47–80. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003360643-4.

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Krasil’ shchik, I. S., and P. H. M. Kersten. "Nonlocal theory." In Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations, 99–153. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-017-3196-6_3.

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Foss, Mikil D., Petronela Radu, and Laura White. "Doubly Nonlocal Cahn–Hilliard Equations." In Association for Women in Mathematics Series, 239–55. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04496-0_10.

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Rodríguez-Bernal, Aníbal, and Silvia Sastre-Gómez. "Nonlinear Nonlocal Reaction-Diffusion Equations." In Advances in Differential Equations and Applications, 53–61. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06953-1_6.

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Тези доповідей конференцій з теми "Nonlocal equations in time"

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Yamazaki, Noriaki. "Optimal control of nonlinear evolution equations associated with time-dependent subdifferentials and applications." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-20.

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2

Hishida, Toshiaki. "THE Navier-stokes flow around a rotating obstacle with time-dependent body force." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-9.

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3

Jakobsen, P. K., P. Ru, and J. V. Moloney. "Nonlocal adiabatic elimination." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.mpp6.

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Анотація:
It is often the case that when studying laser models one is confronted with the problem of stiffness: some of the variables in the problem vary much faster than others. An example of this is standard semiconductor laser models where the time scales in the problem vary from femtoseconds to nanoseconds. For such systems it is a reasonable approach to try to eliminate the fastest variables and only retain them as slaved to the slow variables in the problem. The method of choice in the optics community for realizing the slaving has mostly been standard adiabatic elimination in which the fast variables are slaved by setting the corresponding time derivative to zero and solving for the fast variables. This method has met with reasonable success, but it has been shown that it tends to remove physically relevant instabilities from the reduced mathematical description. For laser models described by ordinary differential equations an application of centremanifold techniques has been shown to retain more of the structure of the full problem. For laser models described by partial differential equations, as is the case if multimode transverse or longitudinal dynamics are studied, the application of centremanifold techniques has so far met with mixed success as it has tended to produce an equation with a singular time behavior. We have developed a new method of adiabatic elimination that is very easy to implement, that is well behaved, that is, free of unphysical instabilities and that reproduces all of the instabilities and dynamics contained in the full system.
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4

Drin, Yaroslav M., I. I. Drin, and S. S. Drin. "Representation of solution for fully nonlocal diffusion equations with deviation time variable." In Correlation Optics 2017, edited by Oleg V. Angelsky. SPIE, 2018. http://dx.doi.org/10.1117/12.2304312.

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5

Nallathambi, K., A. Santhi, and V. Govindan. "Fractional nonlocal integro-differential equations with time-varying generating operators and optimal control." In INTERNATIONAL CONFERENCE ON RECENT TRENDS IN PURE AND APPLIED MATHEMATICS (ICRTPAM-2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0106502.

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Ashyralyev, Allaberen, and Charyyar Ashyralyyev. "Numerical solution of time-nonlocal problem for parabolic equation." In 10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0114878.

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7

Ru, P., P. K. Jakobsen, and J. V. Moloney. "Nonlocal Adiabatic Elimination in the Maxwell-Bloch Equation." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.mc6.

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Анотація:
Adiabatic elimination is a standard procedure applied to the Maxwell-Bloch laser equations when one variable or more is slaved to the remaining variables. An important case in point is a laser with an extremely large gain bandwidth satisfying the condition γ⊥ ≫ γ||, k where γ⊥ is the polarization dephasing rate, γ|| the de-energization rate and k the cavity damping constant. For example, color center gain media satisfy this criterion and support hundreds of thousands of longitudinal modes in synchronous pumped mode-locking operation. For simple single mode plane wave models the crude adiabatic elimination step of setting the derivative of the polarization variable to zero can be avoided by using center manifold techniques [1]. In this general class of singular perturbation problem, the idea is to coordinatize the problem using linear stability analysis about some known solution and then to construct an approximation to the center manifold on which the (possibly dynamic) solution remains for all time. This procedure has been successfully applied to the Maxwell-Bloch equations describing a single mode homogenously broadened ring laser [2]. Extension of the procedure to nonlinear partial differential equations is very difficult in general as the resulting center manifold may be an infinite dimensional object. When transverse (or additional longitudinal) degrees of freedom are introduced in the Maxwell-Bloch equations in order to investigate spatial pattern formation (or mode-locking dynamics) we find that a crude adiabatic elimination (henceforth referred to as standard adiabatic elimination SAE) leads to nonphysical high transverse (or longitudinal) spatial wavenumber instabilities [3]. Recent attempts to apply the center manifold technique to the transverse problem have met with mixed success [4]. In fact the high transverse wavenumber instability shows an even stronger divergence than the SAE case for positive sign of the laser-atom detuning. Moreover, the analysis becomes unwieldy even in situations when the center manifold approach appears to work.
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8

Hamed, M., and K. Saanouni. "Elastoplastic Nonlocal Micromorphic Formulations With Damage Gradient." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82928.

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It is well known that the use of inelastic constitutive equations accounting for induced softening leads to pathological space (mesh) and time discretization dependency of the numerical solution of the Initial and Boundary value Problem (IBVP). To solve this drawback a thermodynamically-consistent formulation incorporating first gradient of micromorphic damage in the framework of micromorphic continuum is proposed. In this formulation the damage field is strongly coupled with mixed isotropic and kinematic nonlinear hardening together with micromorphic damage variables. A new finite element with one additional degree of freedom for the micromorphic damage field is developed and implemented into ABAQUS/EXPLICIT using the user’s subroutines VUEL and VUMAT. For the validation purpose, 3D uniaxial tension example of metallic sheet is performed using the proposed micromorphic fully coupled elastoplastic constitutive equations.
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9

Yang, Ronggui, and Gang Chen. "Two-Dimensional Nanoscale Heat Conduction Using Ballistic-Diffusive Equations." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/htd-24141.

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Abstract It is well recognized that heat conduction in micro- and nanoscale and in ultrafast processes may deviate from the predictions of the Fourier law, due to boundary and interface scattering and the finite relaxation time of heat carriers. The Boltzmann equation is often used with the relaxation time approximation to study classical size effect. However, the solution of Boltzmann equation has been limited to few simple geometrical configurations such as thin films and superlattices. In this paper, we apply the transient ballistic-diffusive equation (BDE) to study the two-dimensional nonlocal phonon transport phenomena. The numerical calculation strategies developed in this paper can be promising for incorporating into commercial device simulator.
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10

Nabelek, Patrik, and Solomon C. Yim. "Riemann-Hilbert Formulation and Solution of Nonlinear Shallow-Water Wave Equations: Nonlocal Dbar Problem as a Unified Approach to Computing Exact Solutions in the Time Domain." In ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/omae2023-108051.

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Abstract Linear wave theories and stochastic linear wave spectra are foundational to ocean and coastal engineering. However, there are some important limitations with linear wave theories, and some of which were originally observed experimentally more than a century ago by John Scott Russell. Nonlinearities will cause the linear wave spectra to evolve in time and space as waves move across a basin, or as waves evolve in the ocean and coastal waters, and in coastal channels. Using a nonlinear wave theory can therefore allow researchers and engineers to better capture the dynamic nature of the ocean waves. Common classical nonlinear wave theories include the (2+1)D KP equation and the (1+1)D Korteweg-de Fries (KdV) equation. As described by Osborne [2010], the invariance nature of these nonlinear wave equations can be characterized in an exact manner by their corresponding nonlinear frequency or wave-number spectrum parallel to the linear case. A nonlocal dbar model was used by Ablowitz, Bar-Yaacov and Fokas [1983], and Zakharov and Manakov [1984] to solve the KP equation by the inverse scattering transform (IST). In this study we discuss the use of the nonlocal dbar problem (NDP) to compute the soliton solutions by the inverse scattering transform, and finite-genus solutions to the KdV equation, and undular bores (dispersive shockwaves). We also discuss the use of NDP to produce soliton solutions and the calculation of periodic finite-genus solutions to the KP equation using Riemann theta functions and complex algebraic geometry.
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Звіти організацій з теми "Nonlocal equations in time"

1

Kunz, Christopher. Nonlocal fractional equations from random walks. Ames (Iowa): Iowa State University, December 2023. http://dx.doi.org/10.31274/cc-20240624-1063.

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2

D'Elia, Marta, Eugenio Aulisa, Giacomo Capodaglio, and Andrea Chierici. Efficient quadrature rules for finite element discretizations of nonlocal equations. Office of Scientific and Technical Information (OSTI), January 2021. http://dx.doi.org/10.2172/1763180.

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3

Worley, P. H. Parallelizing across time when solving time-dependent partial differential equations. Office of Scientific and Technical Information (OSTI), September 1991. http://dx.doi.org/10.2172/6026480.

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Rau, A. Ravi P. Solving time-dependent operator equations for nanoscale physics. Office of Scientific and Technical Information (OSTI), August 2007. http://dx.doi.org/10.2172/913061.

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Gottlieb, David. Spectral Methods for Time Dependent Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, November 1986. http://dx.doi.org/10.21236/ada182809.

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Gottlieb, David. High-Order Time-Domain Methods for Maxwells Equations. Fort Belvoir, VA: Defense Technical Information Center, August 2000. http://dx.doi.org/10.21236/ada387163.

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Hills, Richard G. Addressing Model Form Error for Time-Dependent Conservation Equations. Office of Scientific and Technical Information (OSTI), September 2015. http://dx.doi.org/10.2172/1490528.

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Zhiquiang, C., and J. Jones. Least-Squares Approaches for the Time-Dependent Maxwell Equations. Office of Scientific and Technical Information (OSTI), December 2001. http://dx.doi.org/10.2172/15002754.

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Shang, J. S. Characteristic Based Methods for the Time-Domain Maxwell Equations. Fort Belvoir, VA: Defense Technical Information Center, August 1993. http://dx.doi.org/10.21236/ada272973.

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Perugia, I., D. Schoetzau, and P. Monk. Stabilized Interior Penalty Methods for the Time-Harmonic Maxwell Equations. Fort Belvoir, VA: Defense Technical Information Center, August 2001. http://dx.doi.org/10.21236/ada437465.

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