The asymptotic behavior for neutral stochastic partial functional differential equations

Abstract

ABSTRACTIn this article, we consider the existence and uniqueness, and the asymptotic behavior of the strong solution for the following neutral stochastic partial functional differential equations.where A(t): V → V* is a linear bounded operator. , and are some appropriate measurable functions. By establishing the variational framework, the existence and uniqueness for the strong solution of such equations is shown under the coercivity condition. Then, the asymptotic behavior of the strong solution is investigated and some well-known results are extended. As a by-product, the exponential stability in mean square and almost sure exponential stability for a strong solution of neutral stochastic partial differential equations with delays are also discussed by utilizing the integral inequality. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained results.