[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | All | Home ]

Preprint 2007-010

Global existence and uniqueness of 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 existence and uniqueness of 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. The proof relies on uniform energy estimates for a family of difference approximations: with these estimates at hand we show the existence of a global weak solution. Then, by means of a nontrivial variant of well-known arguments in the literature, uniqueness and optimal regularity are proven. The results of this paper also apply to interaction potentials with non-vanishing negative part and constitute a base for an analysis of the time-asymptotic behaviour.

Available as PDF (191 Kbytes).
Alexander Dressel,
Christian Rohde
Publishing information:
Submitted by:
; 2007-04-26.