Large time asymptotics for the BBM-burgers equation

Nakao Hayashi, Elena I. Kaikina, Pavel I. Naumkin

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We study large time asymptotics of solutions to the BBM-Burgers equation ∂t (u - uxx) + βux - μu xx + uux = 0. We are interested in the large time asymptotics for the case, when the initial data have an arbitrary size. Let the initial data u0 ∈ H1 (R) ∩ W1 1 (R), and θ = ∫R u0 (x) dx ≠ 0. Then we prove that there exists a unique solution u(t, x) ∈ C ([0,\∞); H1 (R) ∩ W11 (R) to the Cauchy problem for the BBM-Burgers equation. We also find the large time asymptotics for the solutions.

Original languageEnglish
Pages (from-to)485-511
Number of pages27
JournalAnnales Henri Poincare
Volume8
Issue number3
DOIs
Publication statusPublished - 2007 Jun

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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