Projects

The Euler equations are a set of hyperbolic partial differential equations that describe the conservation of (usually) internal energy, density, and velocity of a moving, ideal fluid. Ideal here means inviscid and non-heat conducting.

I am interested in investigating how to adapt numerical methods used for control and stabilization of finite dimensional systems to infinite dimensional systems - namely partial differential equations. In particular, I study partial differential equations where the control action is applied to the boundary.

The flow of sediment suspended in a liquid down a slope, although simple sounding, is not well understood mathematically and gives rise to interesting long term behaviors. I am modelling how a slurry of oil and two different types of particles, of the same density and material but different sizes, develops as it flows down an incline.