Research interests
My general research interests are free boundary problems in continuum
mechanics, the mathematical analysis of free boundary problems and the
mathematical modelling of physical and financial processes (using a
continuum approach). Specific interests are:
Phase Change Problems
Phase change problems such as the Stefan problem. The regularisation
of ill-posed phase change problems (and problems relating to the
stability of super-cooled melts, and shape selection during dendritic
growth). Click here for
publications.
Mathematical Finance
Modelling of derivative securities and numerical
solution of option value problems. (American options give rise to free
boundary problems that may be solved using variational inequality
methods.) Many of the models for derivative securities are similar to
phase change problems. Click here
for publications.
Fluid mechanics
Separating flows and vortex sheet free boundaries
in inviscid hydrodynamics. Complex variable and asymptotic approaches
to such problems. Click here for
publications.
Slender, viscous, free-surface flows (jets, sheets
and fibres). The stability of the surfaces and centrelines of such
flows. Effects of gravity, surface tension, inertia on such flows and
their stability. Use of asymptotic methods to make such problems
tractable. Click here for
publications.
Other interests
I am also, occasionally, interested in modelling the behaviour of
redox reaction fronts in porous rock, applications
of asymptotic methods to mathematical problems, the
use of dynamical systems methods for the analysis of
mathematical models and numerical solution of mathematical models.
Click here for
publications.
