Regularity of the semigroups associated with some damped coupled elastic systems II: A nondegenerate fractional damping case. (25th September 2022)

• Record Type: Journal Article
• Authors: Ammari, Kaïs; Shel, Farhat; Tebou, Louis
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 4(2023)
• Page Start: 4289
• Page End: 4302
• Publication Date: 2022-09-25
• Subjects: coupled elastic systems -- fractional damping -- Kelvin–Voigt damping -- semigroup regularity -- structural damping; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8756
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers μ, θ $$ \mu, \theta $$ of the principal operators, with 0 < μ, θ ≤ 1 $$ 0<\mu, \theta \le 1 $$ . 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 $$ 1/2\le \mu, \theta \le 1 $$, the underlying semigroup is analytic. Next, we show that for min ( μ, θ ) ∈ ( 0, 1 / 2 ) $$ \min \left(\mu, \theta \right)\in \left(0, 1/2\right) $$, the semigroup is of certain Gevrey classes. Finally, some examples of application are provided.