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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.

35R60PDEs with randomness, stochastic PDE
60H15Stochastic partial differential equations
93D05Lyapunov and other classical stabilities of control systems
93D20Asymptotic stability of control systems
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