Well-Posedness for a Class of 2×2 Conservation Laws withL∞Data

The Cauchy problem for a special class of 2×2 systems of conservation laws with data inL1∩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 theL1-norm. This solution can be characterized in terms of a Kru kov-type entropy condition, which is introduced here.