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Mark Bowen, Post Doc/Research Associate

Mark Bowen

Please note: Mark has left the Mathematics department at Duke University; some info here might not be up to date.

Contact Info:
Office Location:  029A
Office Phone:  660-2871
Email Address: send me a message
Web Page:


B.Eng. in Electronic Engineering and Mathematics (Joint Honours), Nottingham University, UK, 1995 Ph.D. in Applied Mathematics, University of Nottingham, UK, 1998
Research Interests: Partial and ordinary differential equations, numerical methods and fluid mechanics

NSF-Focused Research Group -- investigating problems in the dynamics of thin viscous films and fluid interfaces.

Thin film theory

I am interested in problems arising from the study of the surface tension driven flow of thin fluid films. The evolution of the film height can modelled by a fourth order degenerate diffusion equation and asymptotics, self-similarity and numerical simulations all play an important role in investigating the behaviour of solutions.

Undercompressive shocks

Recently, experimentalists have shown that undercompressive shocks, which were long thought to be purely a mathematical abstraction, can actually arise in physical problems and this has led to a change in the implication of the term admissible shock. Of particular interest is the numerical modelling of these undercompressive shocks and their stability to small perturbations.

For more information see my research statement.
Curriculum Vitae
Recent Publications

  1. M. Bowen, J. R. King and J. Hulshof, Anomalous exponents and dipole solutions for the thin film equation, SIAM J. Appl. Math., (2001), 62:149-179 [ps]  [abs]
  2. T. P. Witelski and Mark Bowen, ADI schemes for higher-order nonlinear diffusion equations, Appl. Num. Math. (Submitted, 0)
  3. J. R. King and M. Bowen, Moving boundary problems and non-uniqueness for the thin film equation, Euro. J. Appl. Math. (2001), 12:321-356 [ps]  [abs]
  4. J. Hulshof, J. R. King and M. Bowen, Intermediate asymptotics of the porous medium equation with sign changes, Adv. Diff. Eq. (2001), 6:1115-1152 [ps]  [abs]
  5. M. Bowen and J. R. King, Asymptotic behaviour of the thin film equation in bounded domains, Euro. J. Appl. Math. (2001), 12:135-157 [ps]  [abs]
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320