Authors: Michael Reissig; Christiane Reuther
Addresses: Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Prüferstr.9, 09596 Freiberg, Germany ' Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Prüferstr.9, 09596 Freiberg, Germany
Abstract: The goal of this paper is to derive Lp - Lq decay estimates for Klein-Gordon models with an effective mass. We explain first the WKB analysis which leads to a representation of the solution by Fourier multipliers. Then we use stationary phase method to get Lp - Lq decay estimates on the conjugate line. The effective mass allows to derive a Klein-Gordon type decay rate. Some comments to Lp - Lq decay rates for scale-invariant models and for Klein-Gordon models possessing scattering states to wave models complete the paper.
Keywords: time-dependent potential; Klein-Gordon models; decay rates; WKB analysis; stationary phase method; oscillating integrals; modelling; decay estimation; effective mass.
International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.4, pp.323 - 362
Available online: 27 Mar 2013 *Full-text access for editors Access for subscribers Purchase this article Comment on this article