Preprint 1996-044

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

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.