Stabilization of laminated beam with structural damping and a heat conduction of Gurtin–Pipkin's law
Fayssal Djellali
Abstract
In the present work, we analyze the stability properties of a one dimensional thermoelastic laminated beam with structural damping, where the heat conduction is given by Gurtin–Pipkin's law. We show that the associated solution semigroup is exponentially stable if and only if the new introduced stability number χ is null. Furthermore, if χ≠0 we prove the lack of exponential stability. The proofs are based on the energy method and Gearhart–Herbst–Prüss–Huang theorem.
Topics & Concepts
Thermoelastic dampingThermal conductionBeam (structure)MathematicsWork (physics)Stability (learning theory)Mathematical analysisSemigroupPhysicsThermodynamicsThermalOpticsMachine learningComputer scienceStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringThermoelastic and Magnetoelastic Phenomena