Decay for nonlinear Klein-Gordon equations

Vladimir Georgiev, Sandra Lucente

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We study the asymptotic behavior of the semilinear Klein-Gordon equation with nonlinearity of fractional order. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid. In these spaces of fractional order we obtain a weighted Sobolev embedding and a nonlinear estimate. Using these, we establish the decay estimate of the solution for large time provided the power of nonlinearity is greater than a critical value.

Original languageEnglish
Pages (from-to)529-555
Number of pages27
JournalNonlinear Differential Equations and Applications
Volume11
Issue number4
DOIs
Publication statusPublished - 2004 Dec 1
Externally publishedYes

Keywords

  • Semilinear Klein-Gordon equation
  • Weighted Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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