On Some Klein-gordon-schrödinger Type Systems
نویسنده
چکیده
Abstract. We present some recent trends in the theory of Klein-Gordon-Schrödinger type Systems. Then we give some resent results on the following special type of a dissipative Klein-Gordon-Schrödinger System iψt + κψxx + iαψ = φψ, x ∈ Ω, t > 0, φtt − φxx + φ+ λφt = −Reψx, x ∈ Ω, t > 0, satisfying the initial and boundary conditions ψ(x, 0) = ψ0(x), φ(x, 0) = φ0(x), φt(x, 0) = φ1(x), x ∈ Ω, ψ(x, t) = φ(x, t) = 0, x ∈ ∂Ω, t > 0, with κ, α, λ positive constants and Ω a bounded subset of R. This certain system describes the nonlinear interaction between high frequency electron waves and low frequency ion plasma waves in a homogeneous magnetic field. Global existence and uniqueness of solutions are derived. Also necessary conditions for the exponential energy decay of the system are established. Finally, we mention some resent results concerning the asymptotic behavior of this problem under external forces in dimension 1.
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تاریخ انتشار 2007