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Preprint 2007-015

Time-asymptotic behaviour of weak solutions for a viscoelastic two-phase model with nonlocal capillarity

Alexander Dressel and Christian Rohde

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.

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Alexander Dressel,
Christian Rohde
Publishing information:
Submitted by:
; 2007-08-18.