Stability and free energies in linear visco-elasticity

In this paper we show that several free energies can be related to a material with fading memory with different domains of definition and topologies. As Fichera has proved, the study of stability can be affected by the space and then by the topology which we chose, while the material must be independent by this one. In the last part of the work by the semi-group theory, we use the new notion of minimum state to study the asymptotic behavior of the differential system.