## Theory and application of stability for stochastic reaction diffusion systems.(English)Zbl 1148.35106

This paper uses Lyapunov direct method for stochastic partial differential equations. For stochastic reaction-diffusion systems the authors establish Lyapunov stability theory, including stability in probability, asymptotic stability in probability, and exponential stability in mean square.
As the noise is finite dimensional the authors always use Itô’s formula to establish their results.

### MSC:

 35R60 PDEs with randomness, stochastic partial differential equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D20 Asymptotic stability in control theory
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