This paper considers a free boundary problem that describes the motion of contact lines of a liquid droplet on a flat surface. The elliptic nature of the equation for droplet shape and the monotonic dependence of contact line velocity on contact angle allows us to introduce a notion of “viscosity” solutions for this problem. Unlike similar free boundary problems, a comparison principle is only available for a modified short-time approximation because of the constraint that conserves volume. We use this modified problem to construct viscosity solutions to the original problem under a weak geometric restriction on the free boundary shape. We also prove uniqueness provided there is an upper bound on front velocity.
1
University of Arizona, Tucson, United States
2
University of California Los Angeles, United States
Karl Glasner; Inwon C. Kim. Viscosity solutions for a model of contact line motion. Interfaces and free boundaries, Tome 11 (2009) no. 1, pp. 37-60. doi: 10.4171/ifb/203
@article{10_4171_ifb_203,
author = {Karl Glasner and Inwon C. Kim},
title = {Viscosity solutions for a model of contact line motion},
journal = {Interfaces and free boundaries},
pages = {37--60},
year = {2009},
volume = {11},
number = {1},
doi = {10.4171/ifb/203},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/203/}
}
TY - JOUR
AU - Karl Glasner
AU - Inwon C. Kim
TI - Viscosity solutions for a model of contact line motion
JO - Interfaces and free boundaries
PY - 2009
SP - 37
EP - 60
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/203/
DO - 10.4171/ifb/203
ID - 10_4171_ifb_203
ER -
%0 Journal Article
%A Karl Glasner
%A Inwon C. Kim
%T Viscosity solutions for a model of contact line motion
%J Interfaces and free boundaries
%D 2009
%P 37-60
%V 11
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/203/
%R 10.4171/ifb/203
%F 10_4171_ifb_203
