Asymptotic Behavior of Stochastic Reaction–Diffusion Equations

Abstract

In this paper, we concentrate on the propagation dynamics of stochastic reaction–diffusion equations, including the existence of travelling wave solution and asymptotic wave speed. Based on the stochastic Feynman–Kac formula and comparison principle, the boundedness of the solution of stochastic reaction–diffusion equations can be obtained so that we can construct a sup-solution and a sub-solution to estimate the upper bound and the lower bound of wave speed.

Keywords

• stochastic reaction–diffusion equations
• Feynman–Kac formula
• travelling wave
• asymptotic wave speed