Global structure of admissible solutions of multi-dimensional non-homogeneous scalar conservation law with Riemann-type data

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Original languageEnglish
Pages (from-to)1055-1078
Journal / PublicationJournal of Differential Equations
Issue number2
Online published17 Mar 2017
Publication statusPublished - 15 Jul 2017


We investigate the global expression and structure of admissible weak solutions of an n dimensional non-homogeneous scalar conservation law with the initial data that has two constant states, separated by an − 1 dimensional smooth manifold. We obtain the unique global existence of non-self-similar solutions. It is the first result about the global structure of non-self-similar shock waves and rarefaction waves of n dimensional non-homogeneous scalar conservation law. The shock wave and the rarefaction wave can be directly expressed and studied by a global implicit function. Finally, we give some applications to discover some interesting phenomena.

Research Area(s)

  • Multi-dimensional non-homogeneous conservation laws, Non-self-similar solution, Rarefaction wave, Shock wave