Stochastic heat equations on moving domains

Tianyi Pan; Wei Wang; Jianliang Zhai; Tusheng Zhang

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arXiv · 2301.09897

Stochastic heat equations on moving domains

Tianyi Pan·Wei Wang·Jianliang Zhai·Tusheng Zhang

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Abstract

In this paper, we establish the well-posedness of stochastic heat equations on moving domains, which amounts to a study of infinite dimensional interacting systems. The main difficulty is to deal with the problems caused by the time-varying state spaces and the interaction of the particle systems. The interaction still occurs even in the case of additive noise. This is in contrast to stochastic heat equations in a fixed domain.

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Tianyi Pan, Wei Wang, Jianliang Zhai, Tusheng Zhang. 2023-01-24. Stochastic heat equations on moving domains. https://arxiv.org/abs/2301.09897

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