On renormalized dissipative solutions for conservation laws

Satoru Takagi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce a new notion of renormalized dissipative solutions for a scalar conservation law ut+divF(u)=f with locally Lipschitz F and L1 data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bénilan et al. The structure of renormalized dissipative solutions is useful to deal with relaxation systems than the renormalized entropy scheme. As an application of our result, we prove the existence of renormalized dissipative solutions via relaxation.

Original languageEnglish
Pages (from-to)e2483-e2489
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number5-7
Publication statusPublished - 2005 Nov 30


  • Conservation laws
  • Locally Lipschitz continuous
  • Renormalized dissipative solutions
  • Renormalized entropy solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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