Radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions. (November 2017)

• Record Type: Journal Article
• Authors: Nedeljkov, Marko; Neumann, Lukas; Oberguggenberger, Michael; Sahoo, Manas R.
• Is Part Of: Nonlinear analysis. Volume 163(2017)
• Page Start: 104
• Page End: 126
• Publication Date: 2017-11
• Subjects: 35L65 -- 35L67; Pressureless Euler system -- Multidimensional conservation laws -- Radially symmetric solutions -- Shadow waves -- Delta shocks; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.07.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Radially symmetric shadow wave solutions to the system of multidimensional pressureless gas dynamics are introduced, which allow one to capture concentration of mass. The transformation to a one-dimensional system with source terms is performed and physically meaningful boundary conditions at the origin are determined. Entropy conditions are derived and applied to single out physical (nonnegative mass) and dissipative (entropic) solutions. A complete solution to the pseudo-Riemann problem with initial data exhibiting a single delta shock on a sphere is obtained.