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

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. 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.
Publication status:
Published

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Publisher copy:
10.1017/S095679250405418

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
Volume:
15
Issue:
2
Pages:
223-256
Publication date:
2004-04-05
DOI:
EISSN:
1469-4425
ISSN:
0956-7925
URN:
uuid:469dc0f6-cccc-4fdd-8f08-d5eb5c03c85e
Source identifiers:
13883
Local pid:
pubs:13883
Language:
English

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