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

<p style='text-indent:20px;'>We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In case multiplicative noise, existence optimal controls and necessary conditions for optimality are derived. additive we obtain a representation gradient cost functional adjoint calculus. The restriction to noise avoids necessity introducing bac...