An ill-posed Cauchy problem for a hyperbolic system in two space dimensions. (English) Zbl 1114.35123

The author first constructs the solution of the Cauchy problem for a scalar conservation law. Then he presents examples showing that under exactly the same assumptions that guarantee the existence and uniqueness of solutions in the one-dimensional case, in two space dimensions the Cauchy problem is not well posed.
Reviewer: Pavel Rehak (Brno)


35L65 Hyperbolic conservation laws
35D05 Existence of generalized solutions of PDE (MSC2000)
35Q35 PDEs in connection with fluid mechanics
35R25 Ill-posed problems for PDEs
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