Stochastic heat equations with logarithmic nonlinearity

Shijie Shang; Tusheng Zhang

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arXiv · 1907.03948

Stochastic heat equations with logarithmic nonlinearity

Shijie Shang·Tusheng Zhang

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Abstract

In this paper, we establish the existence and uniqueness of solutions to stochastic heat equations with logarithmic nonlinearity driven by Brownian motion on a bounded domain $D$ in the setting of $L^2(D)$ space. The result is valid for all initial values in $L^2(D)$. The logarithmic Sobolev inequality plays an important role.

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Shijie Shang, Tusheng Zhang. 2019-07-09. Stochastic heat equations with logarithmic nonlinearity. https://arxiv.org/abs/1907.03948

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