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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 \(2m\).
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.
On the other hand, we also briefly describe mathematical results and give references on some problems related to, or inspired by, the preceding models.
For the entire collection see [Zbl 0817.00014].

35Q35 PDEs in connection with fluid mechanics
35G25 Initial value problems for nonlinear higher-order PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
76D08 Lubrication theory