Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension

Masakazu Kato, Yu Zhu Wang, Shuichi Kawashima

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We study the initial value problem for the generalized cubic double dispersion equation in one space dimension. We establish a nonlinear approximation result to our global solutions that was obtained in [6]. Moreover, we show that as time tends to infinity, the solution approaches the superposition of nonlinear diffusion waves which are given explicitly in terms of the self-similar solution of the viscous Burgers equation. The proof is based on the semigroup argument combined with the analysis of wave decomposition

Original languageEnglish
Pages (from-to)969-987
Number of pages19
JournalKinetic and Related Models
Volume6
Issue number4
DOIs
Publication statusPublished - 2013 Dec 1
Externally publishedYes

Keywords

  • Asymptotic behavior
  • Burgers equation.
  • Diffusion waves
  • Generalized cubic double dispersion equation
  • Global existence

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation

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