Ecuaciones en derivadas parciales con pertubaciones estocásticas
Non-linear stochastic partial differential equations with delays: existence and uniqueness of solutions.
The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of solutions (in Itô's sense) for a rather general type of stochastic PDE's with non-linear monotone operators and with delays.
Existence and uniqueness of solutions for non-linear stochastic partial differential equations.
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,...
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