Artículo
Existence and Uniqueness of Solutions for Non-Linear Stochastic Partial Differential Equations
Autor/es | Caraballo Garrido, Tomás |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 1991 |
Fecha de depósito | 2015-04-08 |
Publicado en |
|
Resumen | We state some results on existence and uniqueness for the solution of non linear stochastic PDEs
with deviating arguments. In fact, we consider the equation
dx(t) + (A(t; x(t)) + B(t; x(¿ (t))) + f(t)) dt = (C(t; x(½(t))) ... We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. In fact, we consider the equation dx(t) + (A(t; x(t)) + B(t; x(¿ (t))) + f(t)) dt = (C(t; x(½(t))) + g(t)) dwt ; where A(t; :) ; B(t; :) and C(t; :) are suitable families of non linear operators in Hilbert spaces, wt is a Hilbert valued Wiener process, and ¿ ; ½ are functions of delay. If A satisfies a coercivity condition and a monotonicity hypothesis, and if B ; C are Lipschitz continuous, we prove that there exists a unique solution of an initial value problem for the precedent equation. Some examples of interest for the applications are given to illustrate the results. Solutions, Non–Linear Stochastic Partial Differential Equations |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
file_1.pdf | 172.0Kb | [PDF] | Ver/ | |