Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ, 1 with β = max (frac(3, 2), 1 + frac(2, n)) for the nonlinear Klein-Gordon equation with a power nonlinearityut t - Δ u + u = μ | u |σ - 1 u, (t, x) ∈ R × Rn, where 1 + frac(4, n + 2) < σ < 1 + frac(4, n) for n ≥ 3, μ ∈ C.

Original languageEnglish
Pages (from-to)188-199
Number of pages12
JournalJournal of Differential Equations
Volume244
Issue number1
DOIs
Publication statusPublished - 2008 Jan 1

Keywords

  • Asymptotics of solutions
  • Higher space dimensions
  • Nonlinear Klein-Gordon equations
  • Power nonlinearities
  • Scattering operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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