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^*

^*Corresponding author for this work

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

17 Citations (Scopus)

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.

Original language	English
Pages (from-to)	383-395
Number of pages	13
Journal	Journal of Differential Equations
Volume	189
Issue number	2
DOIs	https://doi.org/10.1016/S0022-0396(02)00069-4
Publication status	Published - 2003 Apr 10

Keywords

Comparison
Degenerate elliptic-hyperbolic equation
Entropy solution
Uniqueness
Weak solution

ASJC Scopus subject areas

Analysis

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10.1016/S0022-0396(02)00069-4

Cite this

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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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author = "Kazuo Kobayashi",

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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.

KW - Comparison

KW - Degenerate elliptic-hyperbolic equation

KW - Entropy solution

KW - Uniqueness

KW - Weak solution

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JF - Journal of Differential Equations

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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