Stabilization of a hyperbolic/elliptic system modelling the viscoelastic-gravitational deformation in a multilayered Earth

Abstract

In the last 30 years several mathematical studies have been devoted to the viscoelastic-gravitational coupling in stationary and transient regimes either for static case or for hyperbolic case. However, to the best of our knowledge there is a lack of mathematical study of the stabilization as $t$ goes to infinity of a viscoelastic-gravitational models crustal deformations of multilayered Earth. Here we prove that, under some additional conditions on the data, the difference of the viscoelastic and elastic solutions converges to zero, as $t$ goes to infinity, in a suitable functional space. The proof of that uses a reformulation of the hyperbolic/elliptic system in terms of a nonlocal hyperbolic system.