We concern on the Holmgren-John unique continuation theorem for a visco-elastic equation with a memory term when the coefficients of the equation are analytic. This is a special case of the general unique continuation property (UCP) for the equation if its coefficients are analytic. This equation describes visco-elastic behavior of a medium. In this talk we will present the UCP for the viscoelastic equation when the relaxation tensor is analytic and allowed to be fully anisotropic. We will describe the UCP in terms of a distance defined by
the travel time of the slowest wave associated to the elastic part of this equation.
The collaborators of this study are Maarten de Hoop (Rice University), Matthias Eller (Georgetown University) and Ching-Lung Lin (National Cheng-Kung University).