Estimates of the Domain of Dependence for Scalar Conservation Laws

DOI10.1016/J.JDE.2018.04.015arXiv1707.07456WikidataQ129970846 ScholiaQ129970846MaRDI QIDQ6289357

Publication date: 24 July 2017

Abstract: We consider the Cauchy problem for a multidimensional scalar conservation law and construct an outer estimate for the domain of dependence of its Kruzkov solution. The estimate can be represented as the controllability set of a specific differential inclusion. In addition, reachable sets of this inclusion provide outer estimates for the support of the wave profiles. Both results follow from a modified version of the classical Kruzkov uniqueness theorem, which we also present in the paper. Finally, the results are applied to a control problem consisting in steering a distributed quantity to a given set.

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Attainable sets, reachability (93B03)

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