Time-asymptotic Behaviour of Weak Solutions for a Viscoelastic Two-phase Model with Nonlocal Capillarity

Abstract. The aim of this paper is to study the time-asymptotic behaviour of weak solutions of an initial-boundary value problem for a viscoelastic two-phase material with capillarity in one space dimension. Therein, the capillarity is modelled via a nonlocal interaction potential. Based on the existence and regularity results of [5], we analyze the time-asymptotic convergence of the strain-velocity field. In particular, we will show that, in the time-asymptotic limit, the strain converges pointwise almost everywhere to a stationary solution. The results of this paper also apply for interaction potentials with non-vanishing negative part.