# zbMATH — the first resource for mathematics

Well-posedness for a class of $$2\times 2$$ conservation laws with $$\mathbb{L}^\infty$$ data. (English) Zbl 0892.35097
The following special class od $$2\times 2$$ systems of conservation laws is considered: $$u_t+f(u,v)_x=0$$, $$v_t=0$$. The initial data for these systems are supposed to be in $$L^1\cap L^\infty$$. The existence of a weak solution to such a Cauchy problem is proved in the strictly hyperbolic case. This solution depends continuously in $$L^1$$-norm on initial data and can be characterized in terms of a Kružkov-type entropy condition.
Reviewer: A.Doktor (Praha)

##### MSC:
 35L65 Hyperbolic conservation laws 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35D05 Existence of generalized solutions of PDE (MSC2000) 35L45 Initial value problems for first-order hyperbolic systems
##### Keywords:
Kružkov-type entropy condition
Full Text: