Lack of BV bounds for approximate solutions to the p-system with large data

被引：6

作者：

Bressan, Alberto ^{[1
]}

Chen, Geng ^{[2
]}

Zhang, Qingtian ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 256卷 / 08期

关键词：

NONLINEAR HYPERBOLIC SYSTEMS; CONSERVATION-LAWS; BLOWUP; DECAY;

D O I：

10.1016/j.jde.2014.01.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider front tracking approximate solutions to the p-system of isentropic gas dynamics. At interaction times, the outgoing wave fronts have the same strength as in the exact solution of the Riemann problem, but some error is allowed in their speed. For large BV initial data, we construct examples showing that the total variation of these approximate solutions can become arbitrarily large, or even blow up in finite time. This happens even if the density of the gas remains uniformly positive. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：3067 / 3085

页数：19

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