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

2021/05/29 by Tanja Krunić, Krunić, Tanja, Marko Nedeljkov +1 · 2 citations
Engineering · Mathematics · #35L65 #35L67 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2105.14297

openalex publication_date 2021/05/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Scalar conservation laws with discontinuous flux: existence and uniqueness
• Multidimensional Scalar Conservation Laws with Non-Aligned Discontinuous Flux and Singularity of Solutions

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