Dynamics of stochastic nonlocal reaction–diffusion equations driven by multiplicative noise
Jiaohui Xu, Tomás Caraballo
Abstract
This paper deals with fractional stochastic nonlocal partial differential equations driven by multiplicative noise. We first prove the existence and uniqueness of solution to this kind of equations with white noise by applying the Galerkin method. Then, the existence and uniqueness of tempered pullback random attractor for the equation are ensured in an appropriate Hilbert space. When the fractional nonlocal partial differential equations are driven by colored noise, which indeed are approximations of the previous ones, we show the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as [Formula: see text].
Topics & Concepts
MathematicsStochastic partial differential equationUniquenessMultiplicative noiseMathematical analysisAttractorStochastic differential equationPullback attractorGalerkin methodWhite noisePullbackHilbert spaceMultiplicative functionApplied mathematicsPartial differential equationNonlinear systemDigital signal processingQuantum mechanicsEngineeringAnalog signalPhysicsElectrical engineeringSignal transfer functionStatisticsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringStochastic processes and financial applications