ASYMPTOTIC STABILITY OF RAREFACTION WAVES FOR A HYPERBOLIC SYSTEM OF BALANCE LAWS

Kenta Nakamura; Tohru Nakamura; Shuichi Kawashima

doi:10.3934/KRM.2019035

ASYMPTOTIC STABILITY OF RAREFACTION WAVES FOR A HYPERBOLIC SYSTEM OF BALANCE LAWS

Kenta Nakamura^*, Tohru Nakamura, Shuichi Kawashima

^*Corresponding author for this work

Global Center for Science and Engineering

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

3 Citations (Scopus)

Abstract

This paper is concerned with the rarefaction waves for a model system of hyperbolic balance laws in the whole space and in the half space. We prove the asymptotic stability of rarefaction waves under smallness assumptions on the initial perturbation and on the amplitude of the waves. The proof is based on the L² energy method.

Original language	English
Pages (from-to)	923-944
Number of pages	22
Journal	Kinetic and Related Models
Volume	12
Issue number	4
DOIs	https://doi.org/10.3934/KRM.2019035
Publication status	Published - 2019

Keywords

Asymptotic stability
Energy method
Hyperbolic balance laws
Rarefaction waves

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation

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10.3934/KRM.2019035

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abstract = "This paper is concerned with the rarefaction waves for a model system of hyperbolic balance laws in the whole space and in the half space. We prove the asymptotic stability of rarefaction waves under smallness assumptions on the initial perturbation and on the amplitude of the waves. The proof is based on the L2 energy method.",

keywords = "Asymptotic stability, Energy method, Hyperbolic balance laws, Rarefaction waves",

author = "Kenta Nakamura and Tohru Nakamura and Shuichi Kawashima",

note = "Funding Information: Acknowledgments. We would like to thank the referee for carefully reading our manuscript and for giving valuable comments. This work was partially supported by JSPS KAKENHI Grant Number JP18H01131. Publisher Copyright: {\textcopyright} American Institute of Mathematical Sciences",

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AU - Nakamura, Kenta

AU - Nakamura, Tohru

AU - Kawashima, Shuichi

N1 - Funding Information: Acknowledgments. We would like to thank the referee for carefully reading our manuscript and for giving valuable comments. This work was partially supported by JSPS KAKENHI Grant Number JP18H01131. Publisher Copyright: © American Institute of Mathematical Sciences

PY - 2019

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N2 - This paper is concerned with the rarefaction waves for a model system of hyperbolic balance laws in the whole space and in the half space. We prove the asymptotic stability of rarefaction waves under smallness assumptions on the initial perturbation and on the amplitude of the waves. The proof is based on the L2 energy method.

AB - This paper is concerned with the rarefaction waves for a model system of hyperbolic balance laws in the whole space and in the half space. We prove the asymptotic stability of rarefaction waves under smallness assumptions on the initial perturbation and on the amplitude of the waves. The proof is based on the L2 energy method.

KW - Asymptotic stability

KW - Energy method

KW - Hyperbolic balance laws

KW - Rarefaction waves

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ASYMPTOTIC STABILITY OF RAREFACTION WAVES FOR A HYPERBOLIC SYSTEM OF BALANCE LAWS

Abstract

Keywords

ASJC Scopus subject areas

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