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

Caraballo Garrido, Tomás. "Existence and uniqueness of solutions for non-linear stochastic partial differential equations.." Collectanea Mathematica 42.1 (1991): 51-74. <http://eudml.org/doc/42448>.

@article{CaraballoGarrido1991,
abstract = {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.},
author = {Caraballo Garrido, Tomás},
journal = {Collectanea Mathematica},
keywords = {Ecuaciones diferenciales en derivadas parciales; Ecuaciones diferenciales estocásticas; Ecuaciones diferenciales no lineales; population biology; existence and uniqueness; families of nonlinear operators in Hilbert spaces},
language = {eng},
number = {1},
pages = {51-74},
title = {Existence and uniqueness of solutions for non-linear stochastic partial differential equations.},
url = {http://eudml.org/doc/42448},
volume = {42},
year = {1991},
}

TY - JOUR
AU - Caraballo Garrido, Tomás
TI - Existence and uniqueness of solutions for non-linear stochastic partial differential equations.
JO - Collectanea Mathematica
PY - 1991
VL - 42
IS - 1
SP - 51
EP - 74
AB - 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.
LA - eng
KW - Ecuaciones diferenciales en derivadas parciales; Ecuaciones diferenciales estocásticas; Ecuaciones diferenciales no lineales; population biology; existence and uniqueness; families of nonlinear operators in Hilbert spaces
UR - http://eudml.org/doc/42448
ER -