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Zbl 0839.35102
Bernis, F.
Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems. (English)
[A] 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). ISBN 0-582-25645-3/pbk; ISBN 0-470-23505-5/pbk

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 $2m$.\par One of the purposes of this article is to try to give a concise orientation on some of the physical models and collect references on them.\par On the other hand, we also briefly describe mathematical results and give references on some problems related to, or inspired by, the preceding models.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
35G25 Initial value problems for nonlinear higher-order PDE
35G10 Initial value problems for linear higher-order PDE
35K25 Higher order parabolic equations, general
76D08 Lubrication theory

Keywords: thin viscous flows; nonlinear degenerate parabolic equations; singular elliptic equations; physical models

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