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