REGULARITY AND STABILITY FOR A VISCOELASTIC MATERIAL WITH A SINGULAR MEMORY KERNEL

We consider a linear viscoelastic material whose relaxation function m ay exhibit an initial singularity. We show that the Laplace transform method is still applicable in order to study existence, uniqueness and asymptotic behaviour of the solution to the dynamic problem. In order to provide these results, we impose on the relaxation function only r estrictions deriving from Thermodynamics. Moreover, by using energy es timates, we establish a stability theorem. Finally, for a class of sin gular kernels, we obtain a regularity result which ensures the asympto tic stability of the solution.