Fast-Diffusion Limit for Reaction–Diffusion Equations with Degenerate Multiplicative and Additive Noise

Abstract

In the present work we consider a quite general class of reaction–diffusion equations forced by additive and multiplicative noise. When the diffusion is large, one can approximate the solutions of the stochastic reaction–diffusion equations with polynomial term by the solutions of a stochastic ordinary equations with additive noise. We illustrate our results by applying it to logistic equation and nonlinear heat equation.

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Acknowledgements

The author would like to thank the editor and anonymous reviewers for their precious remarks and suggestions.

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Correspondence to Wael W. Mohammed.

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Mohammed, W.W. Fast-Diffusion Limit for Reaction–Diffusion Equations with Degenerate Multiplicative and Additive Noise. J Dyn Diff Equat 33, 577–592 (2021). https://doi.org/10.1007/s10884-020-09821-y

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Keywords

  • Reaction–diffusion equations
  • Fast diffusion limit
  • Additive noise
  • Multiplicative noise

Mathematics Subject Classification

  • 60H10
  • 60H15
  • 35R60