随机非线性扩散方程障碍问题的适定性：一个熵公式

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-04-18 DOI:10.1016/j.jfa.2025.111012

Kai Du , Ruoyang Liu

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引用次数: 0

摘要

本文建立了一类受保守梯度噪声扰动的退化非线性扩散方程障碍问题的存在唯一性和稳定性结果。我们的方法围绕着引入随机变分不等式的一个新的熵公式。得到了具有非线性反应项的确定性多孔介质方程障碍问题的一个新的适定性结果。

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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Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: An entropy formulation

In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing a new entropy formulation for stochastic variational inequalities. As a consequence, we obtain a novel well-posedness result for the obstacle problem of deterministic porous medium equations with nonlinear reaction terms.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis