Bressan, Alberto An ill-posed Cauchy problem for a hyperbolic system in two space dimensions. (English) Zbl 1114.35123 Rend. Semin. Mat. Univ. Padova 110, 103-117 (2003). 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) Cited in 23 Documents MSC: 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 PDF BibTeX XML Cite \textit{A. Bressan}, Rend. Semin. Mat. Univ. Padova 110, 103--117 (2003; Zbl 1114.35123) Full Text: EuDML arXiv References: [1] A. BRESSAN, Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem, Oxford University Press, 2000. Zbl0997.35002 MR1816648 · Zbl 0997.35002 [2] C. DAFERMOS, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Berlin 1999. Zbl0940.35002 MR1763936 · Zbl 0940.35002 [3] R. DIPERNA - P. L. LIONS, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), pp. 511-517. Zbl0696.34049 MR1022305 · Zbl 0696.34049 · doi:10.1007/BF01393835 · eudml:143741 [4] S. KRUZHKOV, First-order quasilinear equations with several space variables, Math. USSR Sbornik, 10 (1970), pp. 217-273. Zbl0215.16203 · Zbl 0215.16203 · doi:10.1070/SM1970v010n02ABEH002156 [5] E. Y. PANOV, On the theory of generalized entropy solutions of the Cauchy problem for a class of non-strictly hyperbolic systems of conservation laws, Sbornik: Mathematics, 191 (2000), pp. 121-150. Zbl0954.35107 MR1753495 · Zbl 0954.35107 · doi:10.1070/SM2000v191n01ABEH000450 [6] D. SERRE, Systems of Conservation Laws I, II, Cambridge University Press, 2000. Zbl0936.35001 MR1775057 · Zbl 0936.35001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.