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

被引：7

作者：

Nakamura, Kenta ^{[1
]}

Nakamura, Tohru ^{[2
]}

Kawashima, Shuichi ^{[3
]}

机构：

[1] Kyushu Univ, Grad Sch Math, Fukuoka, Fukuoka 8190395, Japan

[2] Kumamoto Univ, Dept Appl Math, Kumamoto 8608555, Japan

[3] Waseda Univ, Fac Sci & Engn, Tokyo 1698555, Japan

来源：

关键词：

Hyperbolic balance laws; rarefaction waves; asymptotic stability; energy method; EQUATIONS; BEHAVIOR;

D O I：

10.3934/krm.2019035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 L-2 energy method.

引用

页码：923 / 944

页数：22

共 18 条

[1] RAREFACTIONS AND LARGE TIME BEHAVIOR FOR PARABOLIC EQUATIONS AND MONOTONE SCHEMES [J].

HARABETIAN, E .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 114 (04) :527-536

[2]

Hattori Y., 1991, JAPAN J IND APPL MAT, V8, P85, DOI DOI 10.1007/BF03167186

[3]

Ilin A.M., 1960, Mat. Sb. (N.S.), V51, P191

[4] MIXED PROBLEMS FOR QUASI-LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS [J].

KAWASHIMA, S ;

YANAGISAWA, T ;

SHIZUTA, Y .

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1987, 63 (07) :243-246

[5] ASYMPTOTIC-BEHAVIOR OF SOLUTIONS FOR THE EQUATIONS OF A VISCOUS HEAT-CONDUCTIVE GAS [J].

KAWASHIMA, S ;

MATSUMURA, A ;

NISHIHARA, K .

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1986, 62 (07) :249-252

[6] ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS OF SYSTEMS FOR ONE-DIMENSIONAL GAS MOTION [J].

KAWASHIMA, S ;

MATSUMURA, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1985, 101 (01) :97-127

[7]

Kawashima S., 2004, Kyushu J. Math., V58, P211, DOI 10.2206/kyushujm.58.211

[8]

Kawashima S., 2002, ADV MATH SCI APPL, V12, P327

[9] Asymptotic Stability of Rarefaction Wave for the Navier-Stokes Equations for a Compressible Fluid in the Half Space [J].

Kawashima, Shuichi ;

Zhu, Peicheng .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 194 (01) :105-132

[10] Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves [J].

Liu, TP ;

Matsumura, A ;

Nishihara, K .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1998, 29 (02) :293-308

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