After successful completion of the course, students are able to give proof for the existence of weak solutions of different classes of nonlinear elliptic and parabolic differential equations; they are able to use maximum principles for weak solutions; furthermore the students learn how to analyze Haniltonian systems, construct solutions for nonlinear wave equations, and to present solutions to a group of other students.

- semilinear elliptic equations

- quasilinear elliptic equations

- semilinear parabolic equations

- quasilinear parabolic equations

- stationary Navier-Stokes-equations

- Schroedinger-equations

- Hamiltonian systems / nontlinear wave equations

There will be lectures and exercises. In the lecture the theory is introduced und examples will be calculated. Once a week there will be exercise-sheets which will be calculated at the blackboard by the students.

Lecture notes are available on the homepage: https://www.asc.tuwien.ac.at/arnold/lehre/nlpdgl/NLpDiff.pdf

timing of the lecture:

* Tu, 13:45-15:00 on zoom:

https://tuwien.zoom.us/j/95209022829?pwd=SzFHOGpNWFJ3OXROS0dMbFA3MWREZz09
Meeting-ID: 952 0902 2829
Passwort: 8u066k38

* We,8:45-10:00 on zoom:

https://tuwien.zoom.us/j/95200126675?pwd=WkI1R1lvbHhYV1lIMXRWQVdBaG1aZz09

Meeting-ID: 952 0012 6675
Passwort: 0p891j50

Exercises and presentation on the blackboard for UE; oral exam for VO

For the oral online exam typically 2 devices with camera (e.g. laptop and smartphone) are needed.

Lecture notes for this course are available; online auf der Homepage des Vortragenden

further references: https://www.asc.tuwien.ac.at/arnold/lehre/nlpdgl/SS2011/

Linear partial differential equations; functional analysis