Abstract
In this paper, we introduce and study a general notion of multivalued solution for nonlinear hyperbolic systems, which need not to be strictly hyperbolic and in conservative form. Then we focus our attention on the system of convervation laws of fluid mechanics with constant pressure which is used in plasma physics. This system is in conservative form but not strictly hyperbolic, and is not solvable in the setting of measurable and bounded single valued functions. However we prove that multivalued solutions in the above sense can be found for this system. Moreover, these solutions are the physically meaningful solutions of the problem.
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Forestier, A., Le Floch, P. Multivalued solutions to some non-linear and non-strictly hyperbolic systems. Japan J. Indust. Appl. Math. 9, 1–23 (1992). https://doi.org/10.1007/BF03167192
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DOI: https://doi.org/10.1007/BF03167192