Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions
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M Akil, A Wehbe
Math. Control Relat. Fields, 2019
academia.edu
In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on a part of the boundary of the domain. First, combining a general criteria of Arendt and Batty with Holmgrens theorem we show the strong stability of our system in the absence of the compactness of the resolvent and without any additional geometric conditions. Next, we show that our system is not uniformly stable in general, since it is the case of the interval. Hence, we look for a polynomial decay rate for smooth initial data for our …
