Regularity of the semigroups associated with some damped coupled elastic systems II: A nondegenerate fractional damping case
Kaïs Ammari, Farhat Shel, Louis Tebou
Abstract
In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers of the principal operators, with . 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 , the underlying semigroup is analytic. Next, we show that for , the semigroup is of certain Gevrey classes. Finally, some examples of application are provided.
Topics & Concepts
SemigroupDegenerate energy levelsMathematicsCoupling (piping)Work (physics)Matrix (chemical analysis)Pure mathematicsMathematical analysisPhysicsQuantum mechanicsMaterials scienceMechanical engineeringComposite materialEngineeringStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems