The initial value problem for the cubic nonlinear Klein-Gordon equation

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

We study the initial value problem for the cubic nonlinear Klein-Gordon equation {utt + u-uxx = μu3,(t, x) R × R, u(0) = u0, ut(0) = u1, x R. where μ R and the initial data are real-valued functions. We obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.

Original languageEnglish
Pages (from-to)1002-1028
Number of pages27
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume59
Issue number6
DOIs
Publication statusPublished - 2008 Nov 1
Externally publishedYes

Keywords

  • Asymptotics of solutions
  • Cubic nonlinear Klein-Gordon equation
  • Initial value problem
  • The inverse wave modified operator

ASJC Scopus subject areas

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

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