On renormalized dissipative solutions for conservation laws

Research output: Contribution to journalArticle

Abstract

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
JournalNonlinear Analysis, Theory, Methods and Applications
Volume63
Issue number5-7
DOIs
Publication statusPublished - 2005 Nov 30

Fingerprint

Conservation Laws
Conservation
Scalar Conservation Laws
Entropy Solution
Entropy
Lipschitz
Equivalence

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On renormalized dissipative solutions for conservation laws. / Takagi, Satoru.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 63, No. 5-7, 30.11.2005.

Research output: Contribution to journalArticle

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