Article ID Journal Published Year Pages File Type
841083 Nonlinear Analysis: Theory, Methods & Applications 2012 10 Pages PDF
Abstract

We consider initial-value problems for semilinear Klein–Gordon equations utt−Δxu+u+f(u)=0 with periodic boundary conditions. Assuming that both the initial data and the nonlinear forcing term f(u)f(u) are analytic, we provide explicit lower bounds on the decay of the radius ρ(t)ρ(t) of analyticity of the solutions as a function of time. In particular, in one space dimension, with uu real valued and f(u)=u2k+1f(u)=u2k+1, we prove that the decay of ρ(t)ρ(t) is not worse than 1/t1/t. The results are given in a general framework, including Gevrey class solutions.

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Physical Sciences and Engineering Engineering Engineering (General)
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