Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations

Satoru Takagi

Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations

Satoru Takagi^*

^*この研究の対応する著者

グローバルエデュケーションセンター

研究成果: Article › 査読

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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.

本文言語	English
ページ（範囲）	481-503
ページ数	23
ジャーナル	Communications in Applied Analysis
巻	9
号	3-4
出版ステータス	Published - 2005 7月

ASJC Scopus subject areas

分析
数値解析
モデリングとシミュレーション
応用数学

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引用スタイル

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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

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