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

2021/09/05 by Kaïs Ammari, Ammari, Kaïs, Farhat Shel +3 · 2 citations
Engineering · Computer Science · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities

paper · pdf · doi:10.48550/arxiv.2109.02044

Abstract

In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers μ, θ, with 0 ≤ μ, θ≤ 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 \citekfl. First, we prove that for 1/2 ≤ μ, θ≤ 1, the underlying semigroup is analytic. Next, we show that for min(μ,θ) ∈ (0,1/2), the semigroup is of certain Gevrey classes. Finally, some examples of application are provided.

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