Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - C. De Lellis

Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions

created on 27 Apr 2003
modified by delellis on 05 May 2011

[BibTeX]

Published Paper

Inserted: 27 apr 2003
Last Updated: 5 may 2011

Journal: International Mathematics Research Notices
Number: 41
Pages: 2205-2220
Year: 2003

Abstract:

In this paper we prove a general existence result for bounded weak solutions of the following class of hyperbolic systems of conservation laws in several space dimensions: \begin{equation}\label{e:Cauchy} \left\{ \begin{array}{l} \partialt ui + \sum\limitsn{\alpha=1} \partial{x\alpha} (f\alpha (
u
) ui) \;=\; 0

ui (0, \cdot) \;=\; \ov{u}i(\cdot)\ , \end{array} \right. \end{equation} where $f\in W^{1,\infty}_{loc} $ and $\ov{u}\in L^\infty$ with $
\ov{u}
\geq c>0$ $\leb^n$-a.e. and $
\ov{u}
\in BV_{loc}$.

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Keywords: existence, conservation laws, Hyperbolic systems, several space dimensions

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