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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)

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
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