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

Publication ,  Journal Article
Witelski, TP; Bernoff, AJ; Bertozzi, AL
Published in: European Journal of Applied Mathematics
April 1, 2004

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.

Duke Scholars

Published In

European Journal of Applied Mathematics

DOI

ISSN

0956-7925

Publication Date

April 1, 2004

Volume

15

Issue

2

Start / End Page

223 / 256

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Witelski, T. P., Bernoff, A. J., & Bertozzi, A. L. (2004). Blowup and dissipation in a critical-case unstable thin film equation. European Journal of Applied Mathematics, 15(2), 223–256. https://doi.org/10.1017/S0956792504005418
Witelski, T. P., A. J. Bernoff, and A. L. Bertozzi. “Blowup and dissipation in a critical-case unstable thin film equation.” European Journal of Applied Mathematics 15, no. 2 (April 1, 2004): 223–56. https://doi.org/10.1017/S0956792504005418.
Witelski TP, Bernoff AJ, Bertozzi AL. Blowup and dissipation in a critical-case unstable thin film equation. European Journal of Applied Mathematics. 2004 Apr 1;15(2):223–56.
Witelski, T. P., et al. “Blowup and dissipation in a critical-case unstable thin film equation.” European Journal of Applied Mathematics, vol. 15, no. 2, Apr. 2004, pp. 223–56. Scopus, doi:10.1017/S0956792504005418.
Witelski TP, Bernoff AJ, Bertozzi AL. Blowup and dissipation in a critical-case unstable thin film equation. European Journal of Applied Mathematics. 2004 Apr 1;15(2):223–256.
Journal cover image

Published In

European Journal of Applied Mathematics

DOI

ISSN

0956-7925

Publication Date

April 1, 2004

Volume

15

Issue

2

Start / End Page

223 / 256

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics