Asymptotic stability in linear viscoelasticity with supplies

Abstract We present some results about the asymptotic behavior of a linear viscoelastic system making use of the approach based on the concept of minimal state. This approach allows to obtain results in a larger class of solutions and data with respect to the classical one based on the histories of the deformation gradient. Recently, a lot of attention has been paid to find unified approaches which permit to study the asymptotic behavior with memory kernels presenting a temporal decay of which the exponential and polynomial decays are only special cases. Here we extend this unified approach to the dynamic problem in presence of supplies by using the minimal state and compare our results with those present in literature.