DAFERMOS REGULARIZATION AND VISCOUS WAVE FAN PROFILES FOR RIEMANN SOLUTIONS OF BURGER'S EQUATION

被引：0

作者：

Liu, Weishi ^{[1
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 3-4期

关键词：

Riemann solutions; Burger's equation; shock waves; rarefaction waves; viscous wave fan profiles; geometric singular perturbations; INVARIANT-MANIFOLDS; EXCHANGE LEMMAS; HYPERBOLIC SYSTEMS; LIMITS;

D O I：

10.3934/dcdss.2023047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider self-similar solutions of the Dafermos regularization of Burger's equation that represent viscous wave fan profiles for Riemann solutions. Two important features of the governing dynamical system are revealed: (i) the existence of a first integral, and (ii) explicit formulas for a normally hyperbolic invariant curve that is a perturbation of the curve of turning points, and for its stable and unstable manifolds. Using (i) and (ii), we obtain a detailed and explicit description of these self-similar solutions.

引用

页码：484 / 497

页数：14

共 5 条

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