Regularity of the semigroups associated with some damped coupled elastic systems II: a nondegenerate fractional damping case

Abstract

In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers $\mu ,\theta$, with $0\le \mu ,\theta \le 1$, of the principal operators. The matrix defining the coupling and damping is nondegenerate. This new work is a sequel to the degenerate case that we discussed recently in \cite{kfl}. First, we prove that for $1/2\le \mu ,\theta \le 1$, the underlying semigroup is analytic. Next, we show that for $\min (\mu ,\theta )\in (0,1/2)$, the semigroup is of certain Gevrey classes. Finally, some examples of application are provided.