Modul

The module will be completed by an oral exam (ca. 20 min).

Graduates will be able to

• name important properties of nonlinear wave equations,
• describe essential difficulties in the analysis of the initial value problem,
• analyze the short- and long-term behavior of solutions of semilinear wave equations using modern techniques.

None

The aim of the course is an introduction to methods for analyzing nonlinear wave equations. The aim is to get to know the basics of various important techniques and to apply them to simple models. The following topics will be covered:

• Symmetries and conservation laws
• Fourier transformation, Sobolev spaces
• Energy estimates
• Strichartz estimates
• Local and global well-posedness results
• Vector field methods
• Longtime behavior

The contents of the module "Functional Analysis" are strongly recommended.

Total workload: 120 hours

Attendance: 45 h

• lectures, problem classes and examination

Self studies: 75 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination