Global existence and optimal time-decay estimates of solutions to the generalized double dispersion equation on the framework of Besov spaces

Yuzhu Wang, Jiang Xu, Shuichi Kawashima

Research output: Contribution to journalArticle


We investigate the initial value problem for the generalized double dispersion equation in any dimensions. Inspired by [28] for the hyperbolic system of first order PDEs, we develop Littlewood-Paley pointwise energy estimates for the dissipative wave equation of high-order. Furthermore, with aid of the frequency-localization Duhamel principle, we establish the global existence and optimal decay estimates of solutions in spatially critical Besov spaces. Our results could hold true for any dimensions (n≥1). Indeed, the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks.

Original languageEnglish
Article number123455
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2020 Jan 1



  • Critical Besov spaces
  • Generalized double dispersion equation
  • Global existence
  • Optimal decay estimates

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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