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Lubrication approximation with prescribed nonzero contact angle. (English) Zbl 0923.35211
Using energy estimates and variational methods, the author proves the long-time existence of a weak solution \(s(t,x)\geq 0\) of the equation \(\partial_ts+ \partial_x(s\partial^3_x s)= 0\) in \(\{s>0\}\), \((\partial_x s)^2= 1\) on \(\partial\{s>0\}\). The equation is a lubrication approximation for the surface tension driven, single phase Hele-Shaw problem with a prescribed contact angle (here \(\pi/4\)).
Reviewer: O.Titow (Berlin)

35R35 Free boundary problems for PDEs
35K65 Degenerate parabolic equations
76D08 Lubrication theory
76D45 Capillarity (surface tension) for incompressible viscous fluids
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