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In this paper, we give positive answer to the open question raised in [E.Zuazua, Exponential decay for the semilinear wave equation with localizeddamping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on theexponential decay of solutions for the semilinear plate equation with localizeddamping.

Exponential decay of solutions for the plate equation with localized damping