Published in

Springer Verlag, Nonlinear Differential Equations and Applications, 4(11), p. 529-555

DOI: 10.1007/s00030-004-2027-z

Links

Tools

Export citation

Search in Google Scholar

Decay for nonlinear Klein-Gordon equations

Journal article published in 2004 by Vladimir Georgiev ORCID, Sandra Lucente
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Upload
Green circle
Postprint: archiving allowed
Upload
Red circle
Published version: archiving forbidden
Policy details
Data provided by SHERPA/RoMEO

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.