On the Structure of Entropy Solutions to the Riemann Problem for a Degenerate Nonlinear Parabolic Equation

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2024-04-06 DOI:10.1007/s10884-024-10361-y

引用次数: 0

Abstract

We find an explicit form of entropy solution to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum point of some strictly convex function of a finite number of variables. We also discuss the limit when piecewise constant coefficients approximate the arbitrary ones.

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论畸变非线性抛物方程黎曼问题的熵解结构

摘要我们为一个具有片断恒定速度和扩散系数的退化非线性抛物方程的黎曼问题找到了一种显式熵解。结果表明，该解对应于有限变量的某个严格凸函数的最小点。我们还讨论了当片断常数系数逼近任意系数时的极限。

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

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.