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arXiv · 2105.14297

Shadow wave solutions for a scalar two-flux conservation law with Rankine-Hugoniot deficit

Tanja Krunić·Marko Nedeljkov
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Abstract

The paper deals with scalar conservation laws having a flux discontinuity at $x=0$ without a weak solution that satisfies the classical Rankine--Hugoniot jump condition at $x=0$. We are using unbounded solutions in the form of shadow waves supported by the origin for solving that problem. The shadow waves are nets of piecewise constant functions approximating a shock wave with added a delta function and sometimes another unbounded part.

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Tanja Krunić, Marko Nedeljkov. 2021-05-29. Shadow wave solutions for a scalar two-flux conservation law with Rankine-Hugoniot deficit. https://arxiv.org/abs/2105.14297

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