Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

Shuichi Kawashima, Yu Zhu Wang

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.

Original languageEnglish
Pages (from-to)233-254
Number of pages22
JournalAnalysis and Applications
Volume13
Issue number3
DOIs
Publication statusPublished - 2015 Jan 1
Externally publishedYes

Keywords

  • asymptotic decay
  • Generalized cubic double dispersion equation
  • global existence
  • linear approximation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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