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The method of characteristics revisited. A viability approach

Jean-Pierre Aubin
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Abstract

This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these results are indeed useful for the treatment of hybrid systems of control theory. We rely on tools forged by set-valued analysis and viability theory, which happen to be both efficient and versatile to cover many problems. They find here unexpected relevance.

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Jean-Pierre Aubin. 1999-06-25. The method of characteristics revisited. A viability approach. https://arxiv.org/abs/math/9906178

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