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- W2959238906 abstract "The following coupled damped Klein-Gordon-Schrödinger equations are considered begin{document}$ begin{eqnarray*} ipsi_t + Delta psi + i alpha b(x)(|psi|^{2} + 1)psi & = & phi psi chi_{omega} ; hbox{in}; Omega times (0, infty), ; (alpha >0) phi_{tt} - Delta phi + a(x) phi_t & = & |psi|^2 chi_{omega}; hbox{in}; Omega times (0, infty), end{eqnarray*} $end{document} where $ Omega $ is a bounded domain of $ mathbb{R}^2 $, with smooth boundary $ Gamma $ and $ omega $ is a neighbourhood of $ partial Omega $ satisfying the geometric control condition. Here $ chi_{omega} $ represents the characteristic function of $ omega $. Assuming that $ a, bin L^{infty}(Omega) $ are nonnegative functions such that $ a(x) geq a_0 >0 $ in $ omega $ and $ b(x) geq b_{0} > 0 $ in $ omega $, the exponential decay rate is proved for every regular solution of the above system. Our result generalizes substantially the previous ones given by Cavalcanti et. al in the reference [9] and [1]." @default.
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- W2959238906 date "2019-01-01" @default.
- W2959238906 modified "2023-10-03" @default.
- W2959238906 title "Exponential stability for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping" @default.
- W2959238906 doi "https://doi.org/10.3934/eect.2019041" @default.
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