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 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 1/2μ, θ 1 , the underlying semigroup is analytic. Next, we show that for min ( μ, θ ) ∈ ( 0, 1 / 2 ) (μ, θ )(0, 1/2) , the semigroup is of certain Gevrey classes. Finally, some examples of application are provided.