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 journalArticlepeer-review

    21 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 2013

    All Science Journal Classification (ASJC) codes

    • Numerical Analysis
    • Modelling and Simulation

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