Energy Decay of Klein-Gordon-Schrödinger Type with Linear Memory Term

where Ω is a bounded domain of R, n ≤ 2 with κ, α, λ > 0. The variable ψ stands for the dimensionless low frequency electron field, whereas φ denotes the dimensionless low frequency density. This system in one dimension describes the nonlinear interaction between high frequency electron waves and low frequency ion plasma waves in a homogeneous magnetic field, adapted to model the UHH plasma heating scheme. The unusual form of the right side of equation (1.2), as compared to the corresponding Zakharov equation, is a consequence of the different low frequency coupling that was considered, i.e. the polarization drift instead of the ponderomotive force.