Dr. Katharina Hopf

Weierstrass Institute for Applied Analysis and Stochastics

Teaching at HU Berlin

I am supervising Master thesis projects in the field of analysis and partial differential equations. To get in touch, please send me an email with a brief description of your interests and a list of the relevant courses you have taken so far.

SoSe 2025: Nonlinear Parabolic Equations and Gradient Flows
Description:
Several important classes of nonlinear evolution equations arising in physics and geometry have the structure of a gradient flow, at least at a formal level. Their solutions can thus be interpreted as curves following the steepest descent of an energy functional with respect to a suitable metric structure. In this course, we explore the intriguing connection between the theory of gradient flows and dissipative evolution equations, with an emphasis on nonlinear parabolic partial differential equations.
Prerequisite: Functional Analysis

Hours: 2+1 SWS.

For preliminary content and literature, see first lecture or Moodle page.


WiSe 2022/23: Nonlinear Partial Differential Equations
Content:
  1. Fixed point theorems
  2. Variational inequalities and quasilinear elliptic equations
  3. Quasilinear parabolic equations and degenerate diffusion
  4. Reaction-diffusion systems
  5. Introduction to hyperbolic systems of conservation laws
Hours: 4+2 SWS.