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Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems. (English) Zbl 0839.35102
Diaz, J. I. (ed.) et al., Free boundary problems: theory and applications. Proceedings of the international conference held in Toledo, Spain, June 21-26, 1993. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 323, 40-56 (1995).
A number of problems and models from thin viscous flows (wetting, draining and coating flows, spreading droplets, thin films, Hele-Shaw systems) lead to higher order nonlinear degenerate parabolic equations and/or singular elliptic equations. Most of the parabolic equations that we consider are of fourth order, although we also mention a sixth-order equation arising in a semiconductor model and some generalizations of order $$2m$$.