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arXiv · 1707.07456

Estimates of the Domain of Dependence for Scalar Conservation Laws

Nikolay Pogodaev
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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.

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Nikolay Pogodaev. 2017-07-24. Estimates of the Domain of Dependence for Scalar Conservation Laws. https://arxiv.org/abs/1707.07456

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