On renormalized dissipative solutions for conservation laws

Satoru Takagi

doi:10.1016/j.na.2005.03.002

On renormalized dissipative solutions for conservation laws

Satoru Takagi^*

^*Corresponding author for this work

Global Education Center

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	e2483-e2489
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	63
Issue number	5-7
DOIs	https://doi.org/10.1016/j.na.2005.03.002
Publication status	Published - 2005 Nov 30

Keywords

Conservation laws
Locally Lipschitz continuous
Renormalized dissipative solutions
Renormalized entropy solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2005.03.002

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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 B{\'e}nilan 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.",

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author = "Satoru Takagi",

year = "2005",

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N2 - 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.

AB - 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.

KW - Conservation laws

KW - Locally Lipschitz continuous

KW - Renormalized dissipative solutions

KW - Renormalized entropy solutions

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 5-7

ER -

On renormalized dissipative solutions for conservation laws

Abstract

Keywords

ASJC Scopus subject areas

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