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Chaotic characterization of one dimensional stochastic fractional heat equation

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  • Gu, Caihong
  • Tang, Yanbin

Abstract

We study the Cauchy problem of the nonlinear stochastic fractional heat equation ∂tu=−ν2(−∂xx)α2u+σ(u)W˙(t,x) on real line R driven by space-time white noise with bounded initial data. We analyze the large-|x| fixed-t behavior of the solution ut(x) for Lipschitz continuous function σ:R→R under three cases. (1) σ is bounded below away from 0. (2) σ is uniformly bounded away from 0 and ∞. (3) σ(x)=cx (the parabolic Anderson model). From the sensitivity to the initial data of stochastic fractional heat equation, we describe that the solution to the Cauchy problem of stochastic fractional heat equation exhibits chaotic behavior at fixed time before the onset of intermittency.

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  • Gu, Caihong & Tang, Yanbin, 2021. "Chaotic characterization of one dimensional stochastic fractional heat equation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001326
    DOI: 10.1016/j.chaos.2021.110780
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    Cited by:

    1. Zhao, Yongqiang & Tang, Yanbin, 2024. "Critical behavior of a semilinear time fractional diffusion equation with forcing term depending on time and space," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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