Abstract.
The following coupled damped Klein-Gordon-Schrödinger equations are considered
where Ω is a bounded domain of \({\mathbb{R}}^{n}, n \leq 3\), with smooth boundary Γ and ω is a neibourhood of \(\partial\Omega\). Here \({\mathcal{X}}_{\omega}\) represents the characteristic function of ω. Assuming that \(a \in W^{1,\infty}(\Omega)\) is a nonnegative function such that \(a(x) \geq a_{0} > 0\) 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].
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M. M. Cavalcanti: Research of M. M. C. partially supported by the CNPq Grant 300631/2003-0
V. N. Domingos Cavalcanti: Research of V. N. D. C. partially supported by the CNPq Grant 304895/2003-2
J. Soriano: Research of J. A. S. partially supported by the CNPq Grant 301352/2003-8
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Bisognin, V., Cavalcanti, M.M., Cavalcanti, V.N.D. et al. Uniform decay for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping. Nonlinear differ. equ. appl. 15, 91–113 (2008). https://doi.org/10.1007/s00030-007-6025-9
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DOI: https://doi.org/10.1007/s00030-007-6025-9