Stochastic quasi-linear partial differential equations of evolution

In this paper we consider a stochastic counterpart of Tosio Kato's quasi-linear partial differential equations and prove the existence and uniqueness of mild solutions.

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Stationary in Distributions of Numerical Solutions for Stochastic Partial Differential Equations with Markovian Switching

Abstract and Applied Analysis ◽

10.1155/2013/752953 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Yi Shen ◽

Yan Li

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Stochastic Partial Differential Equations ◽

Existence And Uniqueness ◽

Numerical Solutions ◽

Mild Solutions ◽

Sufficient Conditions ◽

Markovian Switching ◽

Partial Differential ◽

Stationary Distributions

We investigate a class of stochastic partial differential equations with Markovian switching. By using the Euler-Maruyama scheme both in time and in space of mild solutions, we derive sufficient conditions for the existence and uniqueness of the stationary distributions of numerical solutions. Finally, one example is given to illustrate the theory.

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Foundations of the Theory of Semilinear Stochastic Partial Differential Equations

International Journal of Stochastic Analysis ◽

10.1155/2013/798549 ◽

2013 ◽

Vol 2013 ◽

pp. 1-25

Author(s):

Stefan Tappe

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Stochastic Partial Differential Equations ◽

Existence And Uniqueness ◽

Mild Solutions ◽

Uniqueness Result ◽

Review Article ◽

Banach Fixed Point Theorem ◽

Extended Version ◽

Partial Differential

The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak, and mild solutions, establish their connections, and review a standard existence and uniqueness result. The proof of the existence result is based on a slightly extended version of the Banach fixed point theorem.

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On continuation of Gevrey class solutions of linear partial differential equations

Proceedings of the seventh International Colloquium on Differential Equations ◽

10.1515/9783112319185-027 ◽

1997 ◽

pp. 197-204

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Gevrey Class ◽

Partial Differential ◽

Linear Partial Differential Equations

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Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

Forum Mathematicum ◽

10.1515/forum-2020-0232 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Robert Stegliński

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Conditions ◽

Dirichlet Boundary ◽

Nonlinear Partial Differential Equations ◽

Dirichlet Boundary Conditions ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Lyapunov Inequalities ◽

Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

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Remarks on the Dirichlet problem for general linear partial differential equations

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160110108 ◽

1958 ◽

Vol 11 (1) ◽

pp. 145-151 ◽

Cited By ~ 5

Author(s):

Walter Littman

Keyword(s):

Dirichlet Problem ◽

Partial Differential Equations ◽

Differential Equations ◽

General Linear ◽

Partial Differential ◽

Linear Partial Differential Equations

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DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025706002287 ◽

2006 ◽

Vol 09 (01) ◽

pp. 155-168 ◽

Cited By ~ 6

Author(s):

FULVIA CONFORTOLA

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Hilbert Spaces ◽

Stochastic Partial Differential Equations ◽

Existence And Uniqueness ◽

Backward Stochastic Differential Equations ◽

Uniqueness Result ◽

Infinite Dimensions ◽

Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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On Cauchy's problem for linear partial differential equations of second order in four variables

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160140302 ◽

1961 ◽

Vol 14 (3) ◽

pp. 171-186 ◽

Cited By ~ 1

Author(s):

Leifur Ásgeirsson

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Second Order ◽

Partial Differential ◽

Linear Partial Differential Equations

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Lectures on Cauchy's Problem in Linear Partial Differential Equations

The Mathematical Gazette ◽

10.2307/3603014 ◽

1924 ◽

Vol 12 (171) ◽

pp. 173

Author(s):

P. J. Daniell ◽

J. Hadamard

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Partial Differential ◽

Linear Partial Differential Equations

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Asymptotic solutions of linear partial differential equations of first order having random coefficients

Random Operators and Stochastic Equations ◽

10.1515/rose.1994.2.1.61 ◽

1994 ◽

Vol 2 (1) ◽

Cited By ~ 3

Author(s):

F. HOPPENSTEADT ◽

R. KHASMINSKII ◽

H. SALEHI

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Random Coefficients ◽

Asymptotic Solutions ◽

Partial Differential ◽

First Order ◽

Linear Partial Differential Equations

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Beam Vibrations With Time-Dependent Boundary Conditions

Journal of Applied Mechanics ◽

10.1115/1.4010161 ◽

1950 ◽

Vol 17 (4) ◽

pp. 377-380

Author(s):

R. D. Mindlin ◽

L. E. Goodman

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Conditions ◽

Boundary Value Problems ◽

Separation Of Variables ◽

Boundary Value ◽

Time Dependent ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Vibration Problems

Abstract A procedure is described for extending the method of separation of variables to the solution of beam-vibration problems with time-dependent boundary conditions. The procedure is applicable to a wide variety of time-dependent boundary-value problems in systems governed by linear partial differential equations.

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