Regularity of the semigroups associated with some damped coupled elastic systems II: A nondegenerate fractional damping case. (25th September 2022) - Ammari, Kaïs; Shel, Farhat; Tebou, Louis
Abstract : In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers μ, θ $$ μ, θ $$ of the principal operators, with 0 < μ, θ ≤ 1 $$ 0<μ, θ \le 1 $$ . The matrix defining the coupling and damping is nondegenerate. This new work is a sequel to the degenerate case that we discussed recently. First, we prove that for 1 / 2 ≤ μ, θ ≤ 1 $$ 1/2\le μ, θ \le 1 $$, the underlying semigroup is analytic. Next, we show that for min ( μ, θ ) ∈ ( 0, 1 / 2 ) $$ \min \left(μ, θ \right)\in \left(0, 1/2\right) $$, the semigroup is of certain Gevrey classes. Finally, some examples of application are provided.