WELL-POSEDNESS AND STABILITY OF A LAME SYSTEM WITH INTERNAL FRACTIONAL DAMPING

Abstract

In this paper, we consider polynomial stabilization for a Lam\'e system
in a bounded domain under an internal fractional damping.
We reformulate the system into an augmented model and prove the well-posedness of it by using semigroup method.
Based on a general criteria of Arendt-Batty, we show that the system is strongly stable.
By combining frequency domain method and multiplier techniques, we establish an optimal polynomial energy decay rate.