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On steady states of van der Waals force driven thin film equations

Published online by Cambridge University Press:  01 April 2007

HUIQIANG JIANG  and
WEI-MING NI
HUIQIANG JIANG
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA email: hqjiang@math.umn.edu
WEI-MING NI
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA email: ni@math.umn.edu
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Abstract

Let , N ≥2 be a bounded smooth domain and α > 1. We are interested in the singular elliptic equation with Neumann boundary conditions. In this paper, a complete description of all continuous radially symmetric solutions is given. In particular, we construct nontrivial smooth solutions as well as rupture solutions. Here a continuous solution is said to be a rupture solution if its zero set is nonempty. When N = 2 and α = 3, the equation is used to model steady states of van der Waals force driven thin films of viscous fluids. We also consider the physical problem when total volume of the fluid is prescribed.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 2 , April 2007 , pp. 153 - 180
Copyright
Copyright © Cambridge University Press 2007

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