The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations

Kazuo Kobayashi

doi:10.1016/S0022-0396(02)00069-4

The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations

Kazuo Kobayashi^*

^*この研究の対応する著者

研究成果: Article › 査読

17 被引用数 (Scopus)

抄録

We prove the equivalence of weak solutions and entropy solutions of an elliptic-parabolic-hyperbolic degenerate equation g(t)_t - Δb(u) + div φ(u) = f with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L¹-contraction principle and uniqueness of weak solutions of elliptic-parabolic degenerate equations.

本文言語	English
ページ（範囲）	383-395
ページ数	13
ジャーナル	Journal of Differential Equations
巻	189
号	2
DOI	https://doi.org/10.1016/S0022-0396(02)00069-4
出版ステータス	Published - 2003 4月 10

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abstract = "We prove the equivalence of weak solutions and entropy solutions of an elliptic-parabolic-hyperbolic degenerate equation g(t)t - Δb(u) + div φ(u) = f with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L1-contraction principle and uniqueness of weak solutions of elliptic-parabolic degenerate equations.",

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N2 - We prove the equivalence of weak solutions and entropy solutions of an elliptic-parabolic-hyperbolic degenerate equation g(t)t - Δb(u) + div φ(u) = f with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L1-contraction principle and uniqueness of weak solutions of elliptic-parabolic degenerate equations.

AB - We prove the equivalence of weak solutions and entropy solutions of an elliptic-parabolic-hyperbolic degenerate equation g(t)t - Δb(u) + div φ(u) = f with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L1-contraction principle and uniqueness of weak solutions of elliptic-parabolic degenerate equations.

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KW - Degenerate elliptic-hyperbolic equation

KW - Entropy solution

KW - Uniqueness

KW - Weak solution

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The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations

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