The Cauchy problem for a special class of 2 × 2 systems of conservation laws with data in L1 ∩ L∞ 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 L1-norm. This solution can be characterized in terms of a Kružkov-type entropy condition, which is introduced here.
All Science Journal Classification (ASJC) codes
- Applied Mathematics