DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

doi:10.1016/S0252-9602(12)60138-6

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1743-1758.doi: 10.1016/S0252-9602(12)60138-6

DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

肖清华|陈正争*

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2011-07-06 修回日期:2011-10-12 出版日期:2012-09-20 发布日期:2012-09-20
通讯作者: 陈正争，chenzzandu@163.com E-mail:qhxiaoll@126.com; chenzzandu@163.com
基金资助:
This work was supported by the “Fundamental Research Funds for the Central Universities” and the National Natural Science Foundation of China (10871151).

DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

XIAO Qing-Hua, CHEN Zheng-Zheng*

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2011-07-06 Revised:2011-10-12 Online:2012-09-20 Published:2012-09-20
Contact: CHEN Zheng-Zheng，chenzzandu@163.com E-mail:qhxiaoll@126.com; chenzzandu@163.com
Supported by:
This work was supported by the “Fundamental Research Funds for the Central Universities” and the National Natural Science Foundation of China (10871151).

摘要/Abstract

摘要：

This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation to the cor-responding degenerate boundary layer solutions in the half-space. It is shown that the convergence rate is t^−α/4 as t →1 provided that the initial perturbation lies in H¹α for α < α(q) := 3+ 2/q , where q is the degeneracy exponent of the flux function. Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1].

关键词: generalized BBM-Burgers equation, degenerate boundary layer solutions, convergence rates, Hardys inequality, space-time weighted energy method

Abstract:

Key words: generalized BBM-Burgers equation, degenerate boundary layer solutions, convergence rates, Hardys inequality, space-time weighted energy method

中图分类号:

34K21

肖清华, 陈正争. DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION[J]. 数学物理学报(英文版), 2012, 32(5): 1743-1758.

XIAO Qing-Hua, CHEN Zheng-Zheng. DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION[J]. Acta mathematica scientia,Series B, 2012, 32(5): 1743-1758.

参考文献

[1] Kawashima S, Kurata K. Hardy type inequality and application to the stability of degenerate stationary waves. J Funct Anal, 2009, 257: 1–19

[2] Kagei Y, Kawashima S. Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space. Commun Math Phys, 2006, 266: 401–430

[3] Kawashima S, Nishibata S, Nishikawa M. Lp energy method for multi-dimensional viscous conservation laws and application to the stability of planar waves. J Hyperbolic Differ Equ, 2004, 1: 581–603

[4] Liu T P, Matsmura A, Nishihara K. Behavior of solutions for the Burgers equations with boundary corre-sponding to rarefaction waves. SIAM J Math Anal, 1998, 29: 293–308

[5] Nakamura M, Nishibata S, Yuge T. Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equations in a half line. J Differ Equ, 2007, 241(1): 94–111

[6] Ueda Y. Asymptotic stability of the stationary solution for damped wave equations with a nonlinear convection term. Adv Math Sci Appl, 2008, 18(1): 329–343

[7] Ueda Y, Nakamura T, Kawashima S. Stability of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space. Kinetic Related Models, 2008, 1: 49–64

[8] Ueda Y, Nakamura T, Kawashima S. Stability of degenerate stationary waves for viscious gas. Arch Rational Mech Anal, 2010, 198(3): 735–762

[9] Yin H, Zhao H J, Kim J. Convergence rates of solutions toward boundary layer solutions for generalized Benjamin-Bona-Mahony-Burgers equations in the half-space. J Differ Equ, 2008, 245: 3144–3216

[10] Yin H, Zhao H J. Nonlinear stability of boundary layer solutions for generalized Benjamin-Bona-Mahony-Burgers equation in the half space. Kinetic Related Models, 2009, 2(3): 521–550

DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

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