Stability of solutions to stochastic partial differential equations

Exponential stability of mild solutions to impulsive stochastic neutral partial differential equations with memory

*Correspondence: [email protected]; [email protected] 1School of Mathematics & Computer Science, Wuhan Polytechnic University, Wuhan, Hubei, China 2School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China Abstract In this paper, we study the exponential stability in the pth moment of mild solutions to impulsive stochastic neutral partial differential e...

Existence and Stability of Mild Solutions to Impulsive Stochastic Neutral Partial Functional Differential Equations

In this article, we study a class of impulsive stochastic neutral partial functional differential equations in a real separable Hilbert space. By using Banach fixed point theorem, we give sufficient conditions for the existence and uniqueness of a mild solution. Also the exponential p-stability of a mild solution and its sample paths are obtained.

Topological soliton solutions of the some nonlinear partial differential equations

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

Stochastic Partial Differential Equations

Taylor expansions of solutions of stochastic partial differential equations

The solutions of parabolic and hyperbolic stochastic partial differential equations (SPDEs) driven by an infinite dimensional Brownian motion, which is a martingale, are in general not semi-martingales any more and therefore do not satisfy an Itô formula like the solutions of finite dimensional stochastic differential equations (SODEs). In particular, it is not possible to derive stochastic Tay...