Stochastic heat equations with logarithmic nonlinearity

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.

30 pages

Cited by in corpus (1)

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