  We study the stability of reaction-diffusion equations in presence of noise.
The relationship of stability of solutions between the stochastic ordinary
different equations and the corresponding stochastic reaction-diffusion
equation is firstly established. Then, by using the Lyapunov method, sufficient
conditions for mean square and stochastic stability are given. The results show
that the multiplicative noise can make the solution stable, but the additive
noise will be not.
