Young-measure solutions for multidimensional systems of conservation laws

Pablo Pedregal

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arXiv · 1810.09326

Young-measure solutions for multidimensional systems of conservation laws

Pablo Pedregal

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Abstract

We explore Young measure solutions of systems of conservation laws through an alternative variational method that introduces a suitable, non-negative error functional to measure departure of feasible fields from being a weak solution. Young measure solutions are then understood as being generated by minimizing sequences for such functional much in the same way as in non-convex, vector variational problems. We establish an existence result for such generalized solutions based on an appropriate structural condition on the system. We finally discuss how the classic concept of a Young measure solution can be improved, and support our arguments by considering a scalar, single equation in dimension one.

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Pablo Pedregal. 2018-10-22. Young-measure solutions for multidimensional systems of conservation laws. https://arxiv.org/abs/1810.09326

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