Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation

Vladimir Georgiev, Sandra Lucente

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

In this work we study the decay properties 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: (formula presented) In these spaces of fractional order we obtain a weighted Sobolev inequality and a nonlinear estimate. Using these estimates we study the decay property of the solution for large t provided the power of nonlinearity is greater than a critical value.

Original languageEnglish
Pages (from-to)21-26
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume329
Issue number1
DOIs
Publication statusPublished - 1999 Jul 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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