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

19 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 - Dec 1 2013

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Asymptotic Behavior of Solutions
Nonlinear Approximation
Initial value problems
Nonlinear Diffusion
Self-similar Solutions
Burgers Equation
Global Solution
Superposition
Initial Value Problem
Semigroup
Infinity
Tend
Decomposition
Decompose

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation

Cite this

Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension. / Kato, Masakazu; Wang, Yu Zhu; Kawashima, Shuichi.

In: Kinetic and Related Models, Vol. 6, No. 4, 01.12.2013, p. 969-987.

Research output: Contribution to journalArticle

Kato, Masakazu ; Wang, Yu Zhu ; Kawashima, Shuichi. / Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension. In: Kinetic and Related Models. 2013 ; Vol. 6, No. 4. pp. 969-987.
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