# American Institute of Mathematical Sciences

2007, 2007(Special): 844-854. doi: 10.3934/proc.2007.2007.844

## Global attractor for a Klein-Gordon-Schrodinger type system

 1 Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens, Greece 2 Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens, Hellas, Greece

Received  September 2006 Revised  July 2007 Published  September 2007

In this paper we prove the existence and uniqueness of solutions for the following evolution system of Klein-Gordon-Schrodinger type

$i\psi_t + k\psi_(xx) + i\alpha\psi$ = $\phi\psi + f(x)$,

$\phi_(tt)$ - $\phi_(xx) + \phi + \lambda\phi_t$ = -$Re\psi_x + g(x)$,

$\psi(x,0)=\psi_0(x), \phi(x,0)$ = $\phi_0, \phi_t(x,0)=\phi_1(x)$

$\phi(x,t)=\phi(x,t)=0$, $x\in\partial\Omega, t>0$

where $x \in \Omega, t > 0, k > 0, \alpha > 0, \lambda > 0, f(x)$ and $g(x)$ are the driving terms and $\Omega$ (bounded) $\subset \mathbb{R}$. Also we prove the continuous dependence of solutions of the system on the initial data as well as the existence of a global attractor.

Citation: Marilena N. Poulou, Nikolaos M. Stavrakakis. Global attractor for a Klein-Gordon-Schrodinger type system. Conference Publications, 2007, 2007 (Special) : 844-854. doi: 10.3934/proc.2007.2007.844
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