Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations

Satoru Takagi

Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations

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 the Cauchy problem of a quasilinear anisotropic degenerate parabolic equation u_t + div F(u) = div (A(u)∇ u) +f with locally Lipschitz-continuous flux F and L¹ data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bendahmane and Karlsen. As applications, we apply our result to certain relaxation systems in general L¹-setting and construct a renormalized dissipative solution.

Original language	English
Pages (from-to)	481-503
Number of pages	23
Journal	Communications in Applied Analysis
Volume	9
Issue number	3-4
Publication status	Published - 2005 Jul

ASJC Scopus subject areas

Analysis
Numerical Analysis
Modelling and Simulation
Applied Mathematics

Cite this

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abstract = "We introduce a new notion of renormalized dissipative solutions for the Cauchy problem of a quasilinear anisotropic degenerate parabolic equation ut + div F(u) = div (A(u)∇ u) +f with locally Lipschitz-continuous flux F and L1 data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bendahmane and Karlsen. As applications, we apply our result to certain relaxation systems in general L1-setting and construct a renormalized dissipative solution.",

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AB - We introduce a new notion of renormalized dissipative solutions for the Cauchy problem of a quasilinear anisotropic degenerate parabolic equation ut + div F(u) = div (A(u)∇ u) +f with locally Lipschitz-continuous flux F and L1 data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bendahmane and Karlsen. As applications, we apply our result to certain relaxation systems in general L1-setting and construct a renormalized dissipative solution.

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Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations

Abstract

ASJC Scopus subject areas

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