ボーウェン マーク

I am an applied mathematician undertaking research into nonlinear partial differential equations, employing a combination of analytical and numerical techniques in their study. I am particularly interested in studying free boundary problems arising from thin film flows, including investigations of rupture phenomena and the effects of surface topography and driving forces upon the motion of the liquid. Such problems often yield evolution equations for the interfacial film thickness in the form of high-order degenerate parabolic equations combined with additional convective effects. In certain cases, the solutions to these equations may contain discontinuities; the selection criterion and stability of these ‘shocks’ is also both of mathematical and physical interest.