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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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APA Style

Witelski, T., Bernoff, A., & Bertozzi, A. (2004). Blowup and dissipation in a critical-case unstable thin film equation. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 15(2), 223–256.

MLA Style

Witelski, T, et al. “Blowup and Dissipation in a Critical-Case Unstable Thin Film Equation.” EUROPEAN JOURNAL OF APPLIED MATHEMATICS, vol. 15, no. 2, 2004, pp. 223–56.

Chicago Style

Witelski, T, A Bernoff, and A Bertozzi. 2004. “Blowup and Dissipation in a Critical-Case Unstable Thin Film Equation.” EUROPEAN JOURNAL OF APPLIED MATHEMATICS 15 (2): 223–56.
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Publisher copy:: 10.1017/S095679250405418

Authors

+ Witelski, T More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Bernoff, A More by this author

Role:: Author

+ Bertozzi, A More by this author

Role:: Author

Journal:: EUROPEAN JOURNAL OF APPLIED MATHEMATICS More from this journal
Volume:: 15
Issue:: 2
Pages:: 223-256
Publication date:: 2004-04-01
DOI:: 10.1017/S095679250405418
EISSN:: 1469-4425
ISSN:: 0956-7925

Language:: English
Pubs id:: pubs:13883
UUID:: uuid:469dc0f6-cccc-4fdd-8f08-d5eb5c03c85e
Local pid:: pubs:13883
Source identifiers:: 13883
Deposit date:: 2012-12-19
ARK identifier:: ark:/29072/ora_469dc0f6cccc4fdd8f08d5eb5c03c85e

Terms of use

Copyright date:: 2004

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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