We rigorously prove the convergence of appropriately scaled solutions of the 2D Hele–Shaw moving boundary problem with surface tension in the limit of thin threads to the solution of the formally corresponding Thin Film equation. The proof is based on scaled parabolic estimates for the nonlocal, nonlinear evolution equations that arise from these problems.
1
Leibniz University Hannover, Germany
2
TU Eindhoven, Netherlands
Bogdan-Vasile Matioc; Georg Prokert. Hele–Shaw flow in thin threads: A rigorous limit result. Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 205-230. doi: 10.4171/ifb/280
@article{10_4171_ifb_280,
author = {Bogdan-Vasile Matioc and Georg Prokert},
title = {Hele{\textendash}Shaw flow in thin threads: {A} rigorous limit result},
journal = {Interfaces and free boundaries},
pages = {205--230},
year = {2012},
volume = {14},
number = {2},
doi = {10.4171/ifb/280},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/280/}
}
TY - JOUR
AU - Bogdan-Vasile Matioc
AU - Georg Prokert
TI - Hele–Shaw flow in thin threads: A rigorous limit result
JO - Interfaces and free boundaries
PY - 2012
SP - 205
EP - 230
VL - 14
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/280/
DO - 10.4171/ifb/280
ID - 10_4171_ifb_280
ER -
%0 Journal Article
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%T Hele–Shaw flow in thin threads: A rigorous limit result
%J Interfaces and free boundaries
%D 2012
%P 205-230
%V 14
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/280/
%R 10.4171/ifb/280
%F 10_4171_ifb_280
