### Well-Posedness for a Class of $2\times 2$ Conservation Laws with $L^\infty$ data

Paolo Baiti and Helge Kristian Jenssen

Abstract: The Cauchy problem for a special class of $2\times 2$ systems of conservation laws with data in $L^1\cap L^\infty$ is considered. In the strictly hyperbolic case we prove the existence of a weak solution which depends continuously on the initial data with respect to the $L^1$-norm. This solution can be characterized in terms of a Kru{\v{z}}kov-type entropy condition, which is here introduced.

Paper:
Available as PostScript
Title:
Well-Posedness for a Class of $2\times 2$ Conservation Laws with $L^\infty$ data
Author(s):
Paolo Baiti, <baiti@sissa.it>
Helge Kristian Jenssen <jenssen@math.ntnu.no>
Publishing information:
Submitted to Journal of Differential Equations
Submitted by:
<helgekj@math.ntnu.no> December 16 1996.

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