Viscous singular shock profiles for a system of conservation laws modeling two-phase flow

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Hsu, Ting-Hao¹ 

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

关键词: Conservation laws;    Singular shocks;    Viscous profiles;    Dafermos regularization;    Geometric Singular Perturbation Theory;   

DOI  :  10.1016/j.jde.2016.04.034

来源: Elsevier

【 摘 要 】

This paper is concerned with singular shocks for a system of conservation laws via the Dafermos regularization u(t) + f (u)(x) = epsilon tu(xx). For a system modeling incompressible two-phase fluid flow, the existence of viscous profiles is proved using Geometric Singular Perturbation Theory. The weak convergence and the growth rate of the viscous solution are also derived; the weak limit is the sum of a piecewise constant function and a delta-measure supported on a shock line, and the maximum value of the viscous solution is of order exp (1/epsilon). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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