Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10426866 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 15 Pages |
Abstract
In this paper we study the long time behavior of solutions for the following system of Klein-Gordon-Schrödinger type iÏt+κÏxx+iαÏ=ÏÏ+f,ÏttâÏxx+Ï+λÏt=âReÏx+g,Ï(x,0)=Ï0(x),Ï(x,0)=Ï0(x),Ït(x,0)=Ï1(x),limxâ±âÏ(x,t)=limxâ±âÏ(x,t)=0,t>0, where xâR,κ>0,α>0,λ>0. First, the existence, uniqueness and continuity of the solutions on the initial data are proved. Then the asymptotic compactness of the solutions and the existence of a global compact attractor are shown.
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Authors
Marilena N. Poulou, Nikolaos M. Stavrakakis,