Limiting dynamics for stochastic nonclassical diffusion equations

Peng Gao

doi:10.3934/dcdsb.2021288

Article Contents

2022, Volume 27, Issue 10: 5597-5629. Doi: 10.3934/dcdsb.2021288

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Limiting dynamics for stochastic nonclassical diffusion equations

Peng Gao

School of Mathematics and Statistics, and Center for Mathematics, and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China

Received: May 31, 2021

Revised: September 30, 2021

Early access: December 2021

Published: October 2022

Peng Gao is supported by the Fundamental Research Funds for the Central Universities (2412020FZ022)

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Abstract

In this paper, we are concerned with the dynamical behavior of the stochastic nonclassical parabolic equation, more precisely, it is shown that the inviscid limits of the stochastic nonclassical diffusion equations reduces to the stochastic heat equations. The key points in the proof of our convergence results are establishing some uniform estimates and the regularity theory for the solutions of the stochastic nonclassical diffusion equations which are independent of the parameter. Based on the uniform estimates, the tightness of distributions of the solutions can be obtained.

Keywords:

Inviscid limits,
Singular perturbation,
Stochastic nonclassical diffusion equation,
Stochastic heat equation.

Mathematics Subject Classification: Primary: 60H15, 35K70; Secondary: 35Q35, 35A01.

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