The main goal in this work is to prove the exponential decay of the semigroup associated with a t... more The main goal in this work is to prove the exponential decay of the semigroup associated with a thermoelastic system composed of an Euler-Bernoulli type equation that models the transverse oscillation of a homogeneous microbeam with axial movement and in which a viscous damping is acting. In addition, to this microbeam has been endowed with a thermal effect given by the Coleman-Gurtin model which depends essentially on past history, representing an improvement of Fourier, Cattaneo and Green-Naghdi models. To achieve this goal, we will use mainly multiplicative techniques and standard tools of functional analysis.
The main goal in this work is to prove the exponential decay of the semigroup associated with a t... more The main goal in this work is to prove the exponential decay of the semigroup associated with a thermoelastic system composed of an Euler-Bernoulli type equation that models the transverse oscillation of a homogeneous microbeam with axial movement and in which a viscous damping is acting. In addition, to this microbeam has been endowed with a thermal effect given by the Coleman-Gurtin model which depends essentially on past history, representing an improvement of Fourier, Cattaneo and Green-Naghdi models. To achieve this goal, we will use mainly multiplicative techniques and standard tools of functional analysis.
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