Diffusive limits of nonlinear hyperbolic systems with variable coefficients

Hironari Miyoshi; Masayoshi Tsutsumi

doi:10.1007/s00161-016-0497-y

Diffusive limits of nonlinear hyperbolic systems with variable coefficients

Hironari Miyoshi^*, Masayoshi Tsutsumi

^*Corresponding author for this work

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

Abstract

We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.

Original language	English
Pages (from-to)	1583-1599
Number of pages	17
Journal	Continuum Mechanics and Thermodynamics
Volume	28
Issue number	5
DOIs	https://doi.org/10.1007/s00161-016-0497-y
Publication status	Published - 2016 Sept 1

Keywords

Carleman’s equation
Diffusive limit
Initial boundary value problem
Nonlinear parabolic equation

ASJC Scopus subject areas

Materials Science(all)
Mechanics of Materials
Physics and Astronomy(all)

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abstract = "We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.",

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author = "Hironari Miyoshi and Masayoshi Tsutsumi",

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AU - Miyoshi, Hironari

AU - Tsutsumi, Masayoshi

PY - 2016/9/1

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N2 - We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.

AB - We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.

KW - Carleman’s equation

KW - Diffusive limit

KW - Initial boundary value problem

KW - Nonlinear parabolic equation

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JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

IS - 5

ER -

Diffusive limits of nonlinear hyperbolic systems with variable coefficients

Abstract

Keywords

ASJC Scopus subject areas

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