The main aim of this course is to show that the Cauchy problem of several hyperbolic linear and non linear PDEs are locally well-posed.
A problem is well-posed if solutions exist in a suitable functional space and these solutions are unique and stable.
In this course, we will show local well-posedness in Sobolev spaces by using energy estimates and the Hahn-Banach theorem.
First, we will show local well-posedness of linear symmetric hyperbolic systems.
Then, we will show that suitable modifications of those results will allow us to prove local well-posedness of linear wave equations.
The last part of the course will focus on non-linear wave equations.
Dr. Yafet Sanchez Sanchez (yess(at)mpim-bonn.mpg.de)
Prof. Dr. Matthias Lesch (lesch(at)math.uni-bonn.de)