Modul

Oral examination of ca. 30 minutes.

The students

• can explain the basics of the theory of strongly continuous operator semigroups and their generators, in particular the theorems on generation and wellposedness, and they can apply it to examples.
• can also describe and use the solution and regularity theory of inhomogeneous Cauchy problems.
• are able to construct analytic semigroups and to characterize their generators. Using these results and perturbations theorems, they can solve partial differential equations.
• are able to explain main aspects of approximation theory of evolution equations.
• can discuss the core statements of stability and spectral theory of operator semigroups and discuss examples by means of them.
• have mastered the important techniques for proofs in evolution equations and are able to, at least, sketch the complicated proofs.

none

• strongly continuous operator semigroups and their generators,
• generation results and wellposedness,
• inhomogeneous Cauchy problems,
• analytic semigroups,
• perturbation and approximation theory,
• stability and spectral theory of operator semigroups,
• applications to partial differential equations

The module “Functional Analysis” is strongly recommended.

Total workload: 240 hours

Attendance: 90 h

• lectures, problem classes and examination

Self studies: 150 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