Large deviations of stochastic heat equations with logarithmic nonlinearity

Tianyi Pan; Shijie Shang; Tusheng Zhang

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arXiv · 2207.02385

Large deviations of stochastic heat equations with logarithmic nonlinearity

Tianyi Pan·Shijie Shang·Tusheng Zhang

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Abstract

In this paper, we establish a large deviation principle for the solutions to the stochastic heat equations with logarithmic nonlinearity driven by Brownian motion, which is neither locally Lipschitz nor locally monotone. Nonlinear versions of Gronwall's inequalities and Log-Sobolev inequalities play an important role.

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Tianyi Pan, Shijie Shang, Tusheng Zhang. 2022-07-06. Large deviations of stochastic heat equations with logarithmic nonlinearity. https://arxiv.org/abs/2207.02385

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