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=SzFHOGpNWFJ3OXROS0dMbFA3MWREZz09Meeting-ID: 952 0902 2829Passwort: 8u066k38
* We,8:45-10:00 on zoom:
https://tuwien.zoom.us/j/95200126675?pwd=WkI1R1lvbHhYV1lIMXRWQVdBaG1aZz09
Meeting-ID: 952 0012 6675Passwort: 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.
Not necessary
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