Stochastic heat equations on moving domains

TL;DR

This paper proves the well-posedness of stochastic heat equations on moving domains, addressing challenges from time-varying spaces and particle interactions, which differ from fixed domain cases.

Contribution

It introduces a framework for analyzing stochastic heat equations on moving domains, handling infinite dimensional interactions and time-dependent state spaces.

Findings

Established well-posedness of stochastic heat equations on moving domains

Addressed interaction complexities in time-varying state spaces

Contrasted with fixed domain stochastic heat equations

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.