Abstract.The following coupled damped Klein-Gordon-Schrödinger equations are consideredwhere Ω is a bounded domain of R n , n ≤ 3, with smooth boundary Γ and ω is a neibourhood of ∂Ω. Here χω represents the characteristic function of ω.Assuming that a ∈ W 1,∞ (Ω) is a nonnegative function such that a(x) ≥ a0 > 0 a. e. in ω, polynomial decay rate is proved for every regular solution of the above system. Our result generalizes substantially the previous results given by the authors in the reference [CDC].
We consider the initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for the coupled system of equations of Korteweg-de Vries (KdV)-type modelling strong interactions between internal solitary waves. Finite domains of wave propagation changing in time arise naturally in certain practical situations when the equations are used as a model for waves and a numerical scheme is needed. We prove a global existence and uniqueness for strong solutions for the coupled system of equations of KdV-type as well as the exponential decay of small solutions in asymptotically cylindrical domains. Finally, we present a numerical scheme based on semi-implicit finite differences and we give some examples to show the numerical effect of the moving boundaries for this kind of systems.
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