The course aims to provide an introduction to the theory of initial boundary value problems for Friedrichs symmetrizable systems, with particular interest for the applications to the equations of ideal Magneto-Hydrodynamics (MHD).
We first analyse different kinds of boundary conditions and present the main results about the well-posedness. In the case of the characteristic boundary, we discuss the possible loss of regularity in the normal direction to the boundary and the use of suitable anisotropic Sobolev spaces in MHD.
Finally, we give a short introduction to the Kreiss-Lopatinskii approach and discuss a simple boundary value problem for the wave equation that may admit estimates with a loss of derivatives from the data.
Further Information
This course is running as part of the National PDE Network Meeting being held in Oxford 18-21 March 2024, and jointly with the 13th Oxbridge PDE conference.
The course is broken into 3 sessions over two days, thus, with all sessions taking place in L2:
16:15-16:55: Short Course II-1 Monday 18 March Characteristic Boundary Problems and Magneto-HydrodynamicsSECCHI-part 1_0.pdf
11:35-12:15: Short Course II-2 Tuesday 19 March Characteristic Boundary Problems and Magneto-Hydrodynamics SECCHI-part 2.pdf
16:15-16:55: Short Course II-3 Tuesday 19 March Characteristic Boundary Problems and Magneto-Hydrodynamics SECCHI-part 3.pdf