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Multi-dimensional scalar balance laws with discontinuous flux

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.

preprint2014arXivOpen access
Piotr GwiazdaAgnieszka Swierczewska-GwiazdaPetra WittboldAleksandra Zimmermann
math.AP
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Open access4 authors1 topic
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Piotr GwiazdaAgnieszka Swierczewska-GwiazdaPetra WittboldAleksandra Zimmermann

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