Partial Differential Equations 2 - Nonlinear Parabolic Evolution Equations

What it is about

You will learn methods of semigroup theory and gradient flows and apply them to investigate both linear and nonlinear parabolic evolution equations. By the end of the module you can analyze existence and qualitative properties of solutions using these techniques.

What you will be able to do

• Application of strongly continuous and analytic semigroup theory
• Use of the Hille–Yosida theorem and the inverse Laplace transform
• Utilization of interpolation spaces for treating mild solutions
• Implementation of gradient-flow methods in Hilbert and metric spaces
• Construction of flows by approximation methods
• Analysis of convergence to equilibrium and geodesic convexity

What the module consists of

• VorlesungThe content is presented, explained, and discussed with examples.
• Übung/Practice sessionsWorking on concrete examples and tasks for deepening and self-check under supervision.

Teaching method

• Vortrag mit Diskussionto convey theory and to stimulate own analyses and literature study
• Übungs-/Praxis-Sitzungento deepen through supervised problem and example work