Dr. Katharina Hopf

Weierstrass Institute for Applied Analysis and Stochastics
Research Group Partial Differential Equations

Current Teaching

Winter term 2022/23: Nonlinear Partial Differential Equations

In winter semester 2022/23, I am teaching the course 'Nonlinear Partial Differential Equations' at the Humboldt University of Berlin (Module M2 of Master of Science in Mathematics).

Information for students

Description:
This course is an advanced course in partial differential equations (PDEs). You will learn some of the key methods to establish existence and uniqueness of solutions to important classes of elliptic, parabolic, and hyperbolic problems, and how to choose appropriate (generalised) solution concepts.
A good part of nonlinear PDE analysis can be obtained by perturbation arguments from the linear theory. However, many of the most intriguing questions in nonlinear PDEs are linked to the structure of the nonlinearity. We aim to illustrate this in several applications.

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:
You should be familiar with the 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. Classical references are, for instance, the books 'Linear Functional Analysis' by H. W. Alt and 'Partial Differential Equations' by L. C. Evans. ]

For further information, please feel free to contact me via email:
hopf(at)wias-berlin.de