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Asymptotic Behavior of Stochastic Reaction–Diffusion Equations

Author

Listed:
  • Hao Wen

    (China Aerodynamics Research and Development Center, No. 6, South Section, Second Ring Road, Mianyang 621000, China)

  • Yuanjing Wang

    (China Aerodynamics Research and Development Center, No. 6, South Section, Second Ring Road, Mianyang 621000, China)

  • Guangyuan Liu

    (China Aerodynamics Research and Development Center, No. 6, South Section, Second Ring Road, Mianyang 621000, China)

  • Dawei Liu

    (China Aerodynamics Research and Development Center, No. 6, South Section, Second Ring Road, Mianyang 621000, China)

Abstract

In this paper, we concentrate on the propagation dynamics of stochastic reaction–diffusion equations, including the existence of travelling wave solution and asymptotic wave speed. Based on the stochastic Feynman–Kac formula and comparison principle, the boundedness of the solution of stochastic reaction–diffusion equations can be obtained so that we can construct a sup-solution and a sub-solution to estimate the upper bound and the lower bound of wave speed.

Suggested Citation

  • Hao Wen & Yuanjing Wang & Guangyuan Liu & Dawei Liu, 2024. "Asymptotic Behavior of Stochastic Reaction–Diffusion Equations," Mathematics, MDPI, vol. 12(9), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1284-:d:1381706
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