Stability in mean of partial variables for stochastic reaction diffusion systems Original Research Article

It is with the aid of the Lyapunov method that stochastic ordinary differential equations and stochastic functional differential equations have been investigated intensively in the past decades. However, for stochastic reaction diffusion equations, this useful technique seems to feel helpless on account of the emptiness of its own Ito’s formula. To get over this difficulty, we will manage to regard the integral of the considered trajectory with respect to spatial variables as the solution of the corresponding stochastic ordinary differential equations and then employ the Ito formula to study stability in mean of partial variables for Ito stochastic reaction diffusion equations. Some sufficient conditions for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, exponential stability in mean of partial variables are presented.