Systems of nonlinear hyperbolic conservation laws model the dynamical behavior of ideal, dissipation-free compressible fluids and plasmas. Due to the nonlinearities, waves may steepen into shocks in finite time. A rich variety of nonlinear wave phenomena may be observed in flows described by hyperbolic conservation laws.

This project involves the theoretical study of nonlinear waves in hyperbolic PDE systems, in particular 'non-strictly hyperbolic' systems for which the various wave speeds may coincide at particular flow states. The equations of ideal magnetohydrodynamics describe such 'non-strictly hyperbolic' system. In particular, you may investigate the behavior of 'simple waves' in model systems with reduced complexity (see the final part of the following presentation: [pdf]). Another possibility is the analytical study of shock wave types in special relativistic magnetized fluids, and the 3D structure of bow shock waves in these fluids (see Hans De Sterck's PhD thesis, where the non-relativistic case was analyzed.) These projects do not necessarily need to include numerical simulation; it can be plain old theoretical applied math for which pen and paper may suffice!

These topics are suitable for PhD or Master's thesis projects. Please contact Hans De Sterck if you are interested.

Created by Hans De Sterck.
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Phone: 1-519-888-4567 ext 7550, Fax: 1-519-746-4319, E-mail: hdesterck@math.uwaterloo.ca.
Office: MC 5016. campus map