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