Can I read Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on Rn on EtoBox?

Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on Rn by Zhang Chen; Bixiang Wang is a Mathematics article available to read on EtoBox.

What is Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on Rn about?

This paper is concerned with periodic measures of fractional stochastic reaction-diffusion equations with variable time delay defined on unbounded domains. We first prove the existence of periodic measures of the Markov process associated with the equation by showing the weak compactness of distribution laws of a family of solutions based on the uniform estimates and the equicontinuity of solutions in probability. We then establish the regularity of periodic measures and prove the tightness of the set of all periodic measures of the equation for small noise intensity. As a result, any sequence of periodic measures possesses at least one limit point, and we further prove every such limit must be a periodic measure of the corresponding limiting system. Finally, under further assumptions on the nonlinear terms, we establish the uniqueness and the exponential mixing property of periodic measures in the sense of Wasserstein metric. All the results of the paper are also valid for invariant measures of the corresponding autonomous version of the stochastic equation with constant time delay. The idea of uniform tail estimates of solutions in probability is employed to overcome the difficul

Who reads Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on Rn?

Author

Zhang Chen; Bixiang Wang

Publisher

Elsevier BV

Published

2022

Language

EN

Field

Mathematics (Physical Sciences)