Large Deviations of Stochastic Heat Equations with Logarithmic Nonlinearity

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-06-11 DOI:10.1007/s11118-024-10142-8

Tianyi Pan, Shijie Shang, Tusheng Zhang

引用次数: 0

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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具有对数非线性的随机热方程的大偏差

在本文中，我们为布朗运动驱动的对数非线性随机热方程的解建立了一个大偏差原理，它既不是局部利普希兹的，也不是局部单调的。非线性版本的 Gronwall 不等式和 Log-Sobolev 不等式发挥了重要作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.