Unique solutions to hyperbolic conservation laws with a strictly convex entropy

Alberto Bressan, Graziano Guerra

Research output: Contribution to journalArticlepeer-review


Consider a strictly hyperbolic n×n system of conservation laws, where each characteristic field is either genuinely nonlinear or linearly degenerate. In this standard setting, it is well known that there exists a Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation. If the system admits a strictly convex entropy, we give a short proof that every entropy weak solution taking values within the domain of the semigroup coincides with a semigroup trajectory. The result shows that the assumptions of “Tame Variation” or “Tame Oscillation”, previously used to achieve uniqueness, can be removed in the presence of a strictly convex entropy.

Original languageEnglish (US)
Pages (from-to)432-447
Number of pages16
JournalJournal of Differential Equations
StatePublished - Apr 5 2024

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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