数学物理学报(英文版) ›› 2002, Vol. 22 ›› Issue (3): 319-328.

• 论文 • 上一篇    下一篇

STABILITY OF THE RAREFACTION WAVE FOR THE GENERALIZED KDV-BURGERS EQUATION

 王治安, 朱长江   

  1. 1Laboratory of Nonlinear Analysis, Department of Mathematics,
    Central China Normal University, Wuhan 430079, China
    2Wuhan Institute of Physics and Mathematics,
    The Chinese Academy of Sciences, Wuhan 430071, China
  • 出版日期:2002-07-15 发布日期:2002-07-15
  • 基金资助:

    The research was supported by the NSFC(10171037).

STABILITY OF THE RAREFACTION WAVE FOR THE GENERALIZED KDV-BURGERS EQUATION

 WANG Zhi-An, ZHU Chang-Jiang   

  1. 1Laboratory of Nonlinear Analysis, Department of Mathematics,
    Central China Normal University, Wuhan 430079, China
    2Wuhan Institute of Physics and Mathematics,
    The Chinese Academy of Sciences, Wuhan 430071, China
  • Online:2002-07-15 Published:2002-07-15
  • Supported by:

    The research was supported by the NSFC(10171037).

摘要:

This paper is concerned with the stability of the rarefaction wave for thegeneralized KdV-Burgers equation ut + f(u)x = μuxx + uxxx, μ > 0,  2 R u|t=0 = u0(x) ! u±, x ! ±1. Roughly speaking, under the assumption that u− < u+, the solution u(x, t) to Cauchy problem (1) satisfying supx2R |u(x, t)−uR(x/t)| ! 0 as t ! 1, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation ut + f(u)x = 0 with Riemann initial data u(x, 0) =(u−, x < 0,u+, x > 0.

关键词: KdV-Burgers equation, rarefaction wave, a priori estimate, L2-energy method

Abstract:

This paper is concerned with the stability of the rarefaction wave for thegeneralized KdV-Burgers equation ut + f(u)x = μuxx + uxxx, μ > 0,  2 R u|t=0 = u0(x) ! u±, x ! ±1. Roughly speaking, under the assumption that u− < u+, the solution u(x, t) to Cauchy problem (1) satisfying supx2R |u(x, t)−uR(x/t)| ! 0 as t ! 1, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation ut + f(u)x = 0 with Riemann initial data u(x, 0) =(u−, x < 0,u+, x > 0.

Key words: KdV-Burgers equation, rarefaction wave, a priori estimate, L2-energy method

中图分类号: 

  • 35L45