Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (3): 319-328.

• Articles • Previous Articles     Next Articles

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).

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

CLC Number: 

  • 35L45
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