The initial formation and structure of two-dimensional diffusive shock waves
type: Item
instance of: scholarly article
title: The initial formation and structure of two-dimensional diffusive shock waves
zbMATH Open document ID: 0596.35085
DOI: 10.1016/S0165-2125(86)80049-X
author: Richard Haberman
published in: Wave Motion
publication date: 1986-01-01T00:00:00Z
review text: The aim of the author is to describe the formation of two-dimensional shock waves for quasilinear partial differential equations with weak dissipation. To this end he considers an equation of the form \[ u_ t+c_ 1(u)u_ x+c_ 2(u)u_ y=\epsilon d(u_{xx}+u_{yy}) \] subject to the following initial condition \(u(x,y,0)=f(x,y)\). He first shows that the characteristics and their singularity where the derivatives of the solution become infinite are described by a generic cubic equation. Then he derives some properties of the singularities.
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 3960107
zbMATH Keywords: Burgers' equation
zbMATH Keywords: Rankine-Hugoniot shock conditions
zbMATH Keywords: caustic
zbMATH Keywords: surface
zbMATH Keywords: quasilinear equation
zbMATH Keywords: two-dimensional shock waves
zbMATH Keywords: weak dissipation
zbMATH Keywords: singularities
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3960107