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The main goal in this work is to prove the exponential decay of the semigroupassociated with a thermoelastic system composed of an Euler-Bernoulli typeequation that models the transverse oscillation of a homogeneous microbeam withaxial movement and in which a viscous damping is acting. In addition, to thismicrobeam has been endowed with a thermal effect given by the Coleman-Gurtinmodel which depends essentially on past history, representing an improvement ofFourier, Cattaneo, and Green-Naghdi models. To achieve these goals, we will usemainly multiplicative techniques and standard tools of functional analysis.

Exponential stability of the Euler-Bernoulli microbeam and thermal effect