Global existence and uniform decay for the coupled Klein-Gordon-Schrödinger equations

Abstract.

This paper is concerned to the existence, uniqueness and uniform decay for the solutions of the coupled Klein-Gordon-Schrödinger damped equations $i\psi_{t} + \Delta\psi + i\ |\psi|^{2}\psi + i\gamma\psi = -\phi\psi\in\Omega \times (0,\infty)$ $\phi_{tt} - \Delta\phi + \mu^{2}\phi + F(\phi, \phi_{t}) = \beta\ |\psi|^{2\theta}\in\Omega \times (0, \infty)$where ω is a bounded domain of R ⁿ, n≤ 3, F : R ²→R is a C ¹-function; γ, β; θ are constants such that γ, β > 0 and 1 ≤ 2θ≤ 2.