Admissibility of self-similar weak solutions of systems of conservation laws in two space variables and time

Michael Sever*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

By means of an example, we postulate that the familiar local entropy conditions on discontinuities are far from sufficient to distinguish admissible weak solutions of systems of conservation laws in two space dimensions and time. We consider the familiar problem of the reflection of an incident shock by a wedge for the "nonlinear wave system", finding a plethora of self-similar weak solutions (or possibly approximate weak solutions) satisfying the usual entropy condition for this system. The multiplicity of such solutions arises from unneeded freedom in the algorithm for constructing solutions, and is directly related to a modest reduction in the assumed regularity of the solution in comparison to that assumed in previous work on this problem. We conclude that if the limit of vanishing viscosity indeed exists for such problems, an additional physical principle is needed to characterize admissible weak solutions.

Original languageEnglish
Pages (from-to)433-481
Number of pages49
JournalJournal of Hyperbolic Differential Equations
Volume6
Issue number3
DOIs
StatePublished - 2009

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