Nonlinear dispersive wave equations in two space dimensions

Nakao Hayashi, Seishirou Kobayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

Abstract

We study the global existence and time decay of solutions to nonlinear dispersive wave equations ∂2 t u + 1/ρ2(-Δ)ρ u = F (∂tu) in two space dimensions, where F (∂tu) = λ∂tup-1∂tu or λ∂tup-, λ∈ C; with p > 2 for 0 < ρ < 1; p > 3 for ρ = 1; and p > 1 + ρ for 1 < ρ < 2: If ρ = 1; then the equation converts into the well-known nonlinear wave equation.

Original languageEnglish
Pages (from-to)1377-1393
Number of pages17
JournalCommunications on Pure and Applied Analysis
Volume14
Issue number4
DOIs
Publication statusPublished - 2015 Jul 1
Externally publishedYes

Keywords

  • Asymptotic behavior
  • Dispersive nonlinear wave
  • Global in time of solutions
  • System of equations
  • Vector field method

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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