Asymptotic behaviour for a thermoelastic problem of a microbeam with thermoelasticity of type III

Abstract

In this paper we study the asymptotic behavior of a equation modeling a microbeam moving transversally, coupled with an equation describing a heat pulse on it. Such pulse is given by a type III of the Green–Naghdi model, providing a more realistic model of heat flow from a physics point of view. We use semigroups theory to prove existence and uniqueness of solutions of our model, and multiplicative techniques to prove exponentially stable of its associated semigroup.

Keywords

• $c_{0}$-semigroup
• functional analysis
• transverse vibration
• coupled system
• exponential stability