401-4767-66L Partial Differential Equations (Hyperbolic PDEs)
|Semester||Autumn Semester 2016|
|Language of instruction||English|
|Abstract||The course begins with characteristics, the definition of hyperbolicity, |
causal structure and the domain of dependence theorem. The course then focuses
on nonlinear systems of equations in two independent variables, in particular the
Euler equations of compressible fluids with plane symmetry and the Einstein equations
of general relativity with spherical symmetry.
|Objective||The objective is to introduce students in mathematics and physics to an area of |
mathematical analysis involving differential geometry which is of fundamental importance
for the development of classical macroscopic continuum physics.
|Content||The course shall begin with the basic structure associated to hyperbolic |
partial differential equations, characteristic hypersurfaces and bicharacteristics,
causal structure, and the domain of dependence theorem. The course shall then focus
on nonlinear systems of equations in two independent variables. The first topic shall be
the Euler equations of compressible fluids under plane symmetry where we shall
study the formation of shocks, and second topic shall be the Einstein equations
of general relativity under spherical symmetry where we shall study the formation of
black holes and spacetime singularities.
|Prerequisites / Notice||Basic real analysis and differential geometry.|