Math @ Duke

Mark Bowen, Post Doc/Research Associate
Please note: Mark has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
 Education:
 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
NSFFocused
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, selfsimilarity 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
 M. Bowen, J. R. King and J. Hulshof, Anomalous exponents and dipole solutions for the thin film equation,
SIAM J. Appl. Math., (2001), 62:149179
[ps] [abs]
 T. P. Witelski and Mark Bowen, ADI schemes for higherorder nonlinear diffusion equations,
Appl. Num. Math.
(Submitted, 0)
 J. R. King and M. Bowen, Moving boundary problems and nonuniqueness for the thin film equation,
Euro. J. Appl. Math. (2001), 12:321356
[ps] [abs]
 J. Hulshof, J. R. King and M. Bowen, Intermediate asymptotics of the porous medium equation with sign changes,
Adv. Diff. Eq. (2001), 6:11151152
[ps] [abs]
 M. Bowen and J. R. King, Asymptotic behaviour of the thin film equation in bounded domains,
Euro. J. Appl. Math. (2001), 12:135157
[ps] [abs]


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

