Existence and uniqueness of solutions for non-linear stochastic partial differential equations

Autores: Tomás Caraballo Garrido
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 42, Fasc. 1, 1991, págs. 51-74
Idioma: inglés
Títulos paralelos:
- Existencia y unicidad de soluciones de ecuaciones diferenciales en derivadas parciales estocáticas no lineales
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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(a(t))) + f(t)dt = (C(t,x(b(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 a, b 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.