Gevrey regularity for the Euler–Bernoulli beam equation with localized structural damping
Matteo Caggio, Filippo Dell’Oro
Abstract
We study a Euler–Bernoulli beam equation with localized discontinuous structural damping. As our main result, we prove that the associated C0-semigroup (S(t))t≥0 is of Gevrey class δ>24 for t>0, hence immediately differentiable. Moreover, we show that (S(t))t≥0 is exponentially stable.
Topics & Concepts
MathematicsBernoulli's principleBeam (structure)Mathematical analysisEuler's formulaPhysicsThermodynamicsOpticsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems