Wave operators to a quadratic nonlinear Klein-Gordon equation in two space dimensions revisited

Nakao Hayashi, Pavel I. Naumkin, Satoshi Tonegawa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We continue to study the existence of the wave operators for the nonlinear Klein-Gordon equation with quadratic nonlinearity in two space dimensions (∂ t 2 - Δ + m 2) u = λu 2, (t,x) ∈ R × R 2. We prove that if, where γ ∈ (0, 1/4) and the norm, then there exist ρ > 0 and T > 1 such that the nonlinear Klein-Gordon equation has a unique global solution u ∈ C([T, ∞); H 1/2 (R 2)) satisfying the asymptotics, for all t > T, where u 0 denotes the solution of the free Klein-Gordon equation.

Original languageEnglish
Pages (from-to)655-673
Number of pages19
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume63
Issue number4
DOIs
Publication statusPublished - 2012 Aug
Externally publishedYes

Keywords

  • Nonlinear Klein-Gordon equations
  • Quadratic nonlinearity
  • Two space dimensions

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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