Convergence Rates to Asymptotic Profile for Solutions of Quasilinear Hyperbolic Equations with Nonlinear Damping

被引：2

作者：

Geng, Shi-feng ^{[1
,2
]}

Wang, Zhen ^{[2
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

[2] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2016年 / 32卷 / 01期

基金：

中国国家自然科学基金;

关键词：

asymptotic behavior; convergence rates; quasilinear hyperbolic equation; nonlinear damping; DIFFUSION WAVES; CONSERVATION-LAWS; P-SYSTEM; BEHAVIOR;

D O I：

10.1007/s10255-015-0535-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The quasilinear hyperbolic equation with nonlinear damping is considered in this paper, a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation, the convergence rates of the new profile are better than that obtained by Nishihara (1997, J. Differential Equations 137, 384-395) and H.-J. Zhao (2000, J. Differential Equations 167, 467-494).

引用

页码：55 / 66

页数：12

共 14 条

[1] HSIAO L, 1993, CHINESE ANN MATH B, V14, P465
[2] CONVERGENCE TO NONLINEAR DIFFUSION WAVES FOR SOLUTIONS OF A SYSTEM OF HYPERBOLIC CONSERVATION-LAWS WITH DAMPING
HSIAO, L
LIU, TP
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 143 (03) : 599 - 605
[3] Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping
Marcati, P
Mei, M
Rubino, B
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2005, 7 (Suppl 2) : S224 - S240
[4] On the diffusive profiles for the system of compressible adiabatic flow through porous media
Marcati, P
Pan, RH
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2001, 33 (04) : 790 - 826
[5] Matsumura A., 1977, Publ. RIMS Kyoto Univ, V13, P349
[6] Nishida T., 1978, Nonlinear hyperbolic equations and related topics in uid dynamics
[7] Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping
Nishihara, K
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 131 (02) : 171 - 188
[8] Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping
Nishihara, K
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 137 (02) : 384 - 395
[9] Lp-convergence rate to nonlinear diffusion waves for p-system with damping
Nishihara, K
Wang, WK
Yang, T
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 161 (01) : 191 - 218
[10] On the diffusion phenomenon of quasilinear hyperbolic waves
Yang, H
Albert, M
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2000, 21 (01) : 63 - 70

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