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Uniqueness of weak solutions of the Cauchy problem for general 2 × 2 conservation laws

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
20
Issue
2
Identifiers
DOI: 10.1016/0022-0396(76)90114-5
Disciplines
  • Mathematics

Abstract

Abstract In this paper we prove uniqueness theorems of the Cauchy problem for general 2 × 2 genuinely nonlinear conservation laws and of isentropic gas dynamics equations, not necessarily convex. We consider solutions which are piecewise continuous and have a finite number of centered rarefaction waves in each compact set. We require the solutions to satisfy an extended entropy condition (E) which reduces to Lax's shock inequalities (L) when the system is genuinely nonlinear.

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