2006/08/07 by Marko Nedeljkov, Nedeljkov, Marko, Michael Oberguggenberger +1
Engineering · Mathematics · #35D05 #35L65 #35L67 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.math/0608184
openalex publication_date 2006/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of a delta shock wave and a singular shock wave was introduced and employed by different authors, and it was shown that a large class of Riemann problems can be solved globally with these additional building blocks. The aim of this paper is to study the interaction of one type of these new solutions, the delta shock waves, with the classical types of solutions. Our model problem is 2 × 2 system derived from a simplified model of magneto-hydrodynamics. The solution concept used in the present paper can be simply described as analogous to the standard one but with L∞-functions substituted by measures in one component of a solution. Here, the delta function is represented by so called two sided delta function. We shall mention only two specific details from the complete interaction result. In some situation the interaction result may contain non-overcompressible delta shock wave called delta contact discontinuity. During delta shock and rarefaction wave interaction it may happen that some Lloc1-function appear.