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

Collectanea Mathematica (1991)

- Volume: 42, Issue: 1, page 51-74
- ISSN: 0010-0757

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topCaraballo 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 -

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