Gevrey Class of Locally Dissipative Euler--Bernoulli Beam Equation
Gerardo Gómez Ávalos, Jaime E. Muñoz Rivera, Z. Liu
Abstract
We study the semigroup associated to the Euler--Bernoulli beam equation with localized (discontinuous) dissipation. We assume that the beam is composed of three components: elastic, viscoelastic of Kelvin--Voigt type, and thermoelastic parts. We prove that this model generates a semigroup of Gevrey class that in particular implies the exponential stability of the model. To our knowledge, this is the first positive result giving increased regularity for the Euler--Bernoulli beam with localized damping.
Topics & Concepts
Thermoelastic dampingSemigroupMathematicsDissipative systemBernoulli's principleBeam (structure)Exponential stabilityEuler's formulaMathematical analysisDissipationViscoelasticityPhysicsNonlinear systemQuantum mechanicsMeteorologyThermalThermodynamicsOpticsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems