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Blowup and dissipation in a critical-case unstable thin film equation

Published online by Cambridge University Press:  07 June 2004

T. P. WITELSKI ,
A. J. BERNOFF  and
A. L. BERTOZZI
T. P. WITELSKI
Affiliation:
Department of Mathematics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708-0320, USA email: witelski@math.duke.edu
A. J. BERNOFF
Affiliation:
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA email: ajb@hmc.edu
A. L. BERTOZZI
Affiliation:
Departments of Mathematics and Physics, Duke University, Durham, NC 27708-0320, USA email: bertozzi@math.duke.edu Current address: Mathematics Department, UCLA, Box 951555, Los Angeles, CA 90095-1555, USA. Email: bertozzi@math.ucla.edu
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Abstract

We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for lubrication flows of thin viscous fluid layers on solid surfaces. %For a special balance between %destabilizing second-order terms and regularizing fourth-order terms, There is a critical mass for blow-up and a rich set of dynamics including families of similarity solutions for finite-time blow-up and infinite-time spreading. The structure and stability of the steady-states and the compactly-supported similarity solutions is studied.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 2 , April 2004 , pp. 223 - 256
Copyright
2004 Cambridge University Press

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