Singular limit of mean-square invariant unstable manifolds for SPDEs driven by nonlinear multiplicative white noise in varying phase spaces

Shi, Lin

doi:10.1090/proc/15992

Singular limit of mean-square invariant unstable manifolds for SPDEs driven by nonlinear multiplicative white noise in varying phase spaces
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Proc. Amer. Math. Soc. 150 (2022), 4407-4419 Request permission

Abstract:

In this paper, we consider a family of stochastic partial differential equations with nonlinear multiplicative white noise. The existence of Lipschitz mean-square random invariant unstable manifolds for these equations has been obtained by Wang [Discrete Contin. Dyn. Syst. 41 (2021), pp. 1449–1468]. Based on this result, we investigate the convergence of Lipschitz mean-square random unstable manifolds for these equations which are defined in varying phase spaces.

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