Dr. Katharina Hopf

Weierstrass Institute for Applied Analysis and Stochastics
Weierstrass Group Multi-species Balance Laws

Teaching

Supervision of final theses
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.

Summer term 2024: X-Student Research Seminar

Supported by the Berlin University Alliance within the programme StuROPx.

Title: Beyond Fick's Law: Pressure-Driven Phenomena in Multi-Species Diffusion

Date and location: Thursdays, 13:00-15:00; Mathematics Institute, HU Berlin.

Relevant links:
Official AGNES entry
Details on registration and participation
AGNES entry with date and location
Project description at Berlin University Alliance webpage

Winter term 2022/23: Nonlinear Partial Differential Equations
HU Berlin
Description:
This course is an advanced Mathematics course (MSc) in partial differential equations. Lecture: 4SWS; Exercise class: 2SWS.

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
Prerequisites:
Content of the Bachelor modules 'Functional Analysis' (M17) and 'Partial Differential Equations' (M18) at HU Berlin. This includes in particular Banach spaces and their dual spaces, weak and strong convergence, compactness, Sobolev spaces (incl. embedding theorems), weak solutions.
[ This material can be found in many textbooks, see e.g. 'Linear Functional Analysis' by H. W. Alt and 'Partial Differential Equations' by L. C. Evans. ]