Title: Lp - Lq decay estimates for Klein-Gordon models with effective mass

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.

DOI: 10.1504/IJDSDE.2012.052842

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.4, pp.323 - 362

Available online: 27 Mar 2013 *

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