Oleinik type estimates and uniqueness for n×n conservation laws

Alberto Bressan, Paola Goatin

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Let ut+f(u)x=0 be a strictly hyperbolic n×n system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of u in a forward neighborhood of each point in the t-x plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleinik in the scalar case.

Original languageEnglish (US)
Pages (from-to)26-49
Number of pages24
JournalJournal of Differential Equations
Volume156
Issue number1
DOIs
StatePublished - Jul 20 1999

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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