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arXiv · 1404.2036

Multi-dimensional scalar balance laws with discontinuous flux

Piotr Gwiazda·Agnieszka Swierczewska-Gwiazda·Petra Wittbold·Aleksandra Zimmermann
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Abstract

We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem is formulated in the framework of multi-valued mappings. We use the notion of entropy-measure valued solutions to prove the so-called contraction principle and comparison principle.

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Piotr Gwiazda, Agnieszka Swierczewska-Gwiazda, Petra Wittbold, Aleksandra Zimmermann. 2014-04-08. Multi-dimensional scalar balance laws with discontinuous flux. https://arxiv.org/abs/1404.2036

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