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Noise and stability in reaction-diffusion equations

  • * Corresponding author: Jinlong Wei

    * Corresponding author: Jinlong Wei 

The authors are grateful to the referees for their valuable suggestions and comments on the original manuscript. This research was partly supported by the NSF of China grants 11771123, 11501577, 11626085 and the Startup Foundation for Introducing Talent of NUIST

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  • 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.

    Mathematics Subject Classification: Primary: 35B35; Secondary: 60H15.


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