Partial Differential Equations 2 - Nonlinear Evolution Equations

What it is about

You deal with qualitative properties of nonlinear evolution equations and learn methods to prove properties of solutions (e.g., regularity gain, convergence to stationary or self-similar profiles, contractivity). The main focuses are variational methods, Hamilton–Jacobi–Bellman equations, systems of conservation laws and degenerate parabolic equations.

What you will be able to do

• Understand variational characterizations of solutions
• Apply variational methods for existence proofs
• Demonstrate regularity gain over time
• Analyze convergence to stationary or self-similar profiles
• Investigate stability properties (e.g., L1-contractivity)

What the module consists of

• LecturePresentation of content, examples and discussion to stimulate independent analyses
• Exercise/PracticumProblem sheets with solutions for deepening; initially guided, later increasingly independent and in small groups

Teaching method

• Lecture with examplesconveys the theoretical concepts and demonstrates applications
• Discussion with studentspromotes understanding and independent analysis
• Exercise sheets with supervised sessionsenable deepening and self-check; conducted progressively independently