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} \partial_t u_i + \sum\limitsⁿ_{\alpha=1} \partial_{x\alpha} (f_\alpha (
u
) u_i) \;=\; 0

u_i (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