Stability of the rarefaction wave for the generalized KdV-Burgers equation

Zhian Wang, Changjiang Zhu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

26 Citations (Scopus)

Abstract

This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation {ut+ f(u)x= μuxx+ δuxxx, μ > 0, δ ∈ R {u|t=0= u0(x) → u±, x → ±∞ Roughly speaking, under the assumption that u-< u+, the solution u(x,t) to Cauchy problem (1) satisfying supx∈R|u(x,t) - uR(x/t)| → 0 as t → ∞, 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.
Original languageEnglish
Pages (from-to)319-328
Number of pages10
JournalActa Mathematica Scientia
Volume22
Issue number3
Publication statusPublished - 1 Jan 2002
Externally publishedYes

Keywords

  • A priori estimate
  • KdV-Burgers equation
  • L -energy method 2
  • Rarefaction wave

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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