NONLINEAR HYPERBOLIC AND DISPERSIVE WAVES

The group is interested in modeling, analysis and the development of computational methods for nonlinear wave hyperbolic and dispersive waves arising in a variety of applications from fluid dynamics, kinetic theory, material science, mathematical biology and geophysics.

From a perspective of applied analysis, members of the team are interested in the theory of conservation laws, the theory of Hamilton-Jacobi equations, and the theory of collisional kinetic models as they arise in dilute gases and in radiative transport. Geometrical optics is a topic of major interest, considered from the viewpoint of kinetic modeling as well as via Lagrangian integrals. There is interest in problems arising from the computation of high frequency densities around caustics and the study of eikonal Hamilton-Jacobi equations with discontinuous Hamiltonians.

There is an ongoing activity on numerical methods for the equations of fluid mechanics, icluding Navier Stokes, shallow water wave equations and gas dynamics. Reasearch interests include the development of finite element algorithms for nonlinear evolution problems, in situations involving shocks and even blow-up patterns for parabolic systems. Also, the computation of complex flows using discontinuous elements, a posteriori estimation and adaptivity, domain decomposition and multigrid.

Members of the group participate in the Research and Training Networks Hyperbolic and kinetic equations (HYKE) and Fronts & Singularities, supported by the "Improving the Human Potential" (IHP) program funded by the European Union.

The group is hosting postdoctoral fellows supported either through the above programs or under the auspices of the MCWAVE Marie Currie "Development Host Fellowships"