Persistence of corners in free boundaries in Hele-Shaw flow
1995 ◽
Vol 6
(5)
◽
pp. 455-490
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Keyword(s):
In this paper we investigate the movement of free boundaries in the two-dimensional Hele-Shaw problem. By means of the construction of special solutions of self-similar type we can describe the evolution of free boundary corners in terms of the angle at the corner. In particular, we prove that, in the injection case, while obtuse-angled corners move and smooth out instantaneously, acute-angled corners persist until a (finite) waiting time at which, at least for the special solutions, they suddenly jump into an obtuse angle, precisely the supplement of the original one. The critical values of the angle π and π/2 are also considered.
1956 ◽
Vol 235
(1202)
◽
pp. 375-381
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1999 ◽
Vol 33
(5)
◽
pp. 939-963
1997 ◽
Vol 8
(4)
◽
pp. 311-329
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Keyword(s):
2011 ◽
Vol 203
(3)
◽
pp. 747-768
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Keyword(s):
2015 ◽
Vol 373
(2050)
◽
pp. 20140276
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Keyword(s):
1996 ◽
Vol 129
(3)
◽
pp. 305-310
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Keyword(s):