Problémy s volnou hranicí a rate-independent systémy
| Thesis title in Czech: | Problémy s volnou hranicí a rate-independent systémy |
|---|---|
| Thesis title in English: | Free boundary problems and rate independent systems |
| Key words: | differential equations|functional analysis|evolutionary problems|existence theory |
| English key words: | differential equations|functional analysis|evolutionary problems|existence theory |
| Academic year of topic announcement: | 2020/2021 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | doc. Sebastian Schwarzacher, Dr. |
| Author: |
| Guidelines |
| Rate independent systems are time dependent processes, with the property to react with infinite speed on its environment. It has many applications, whenever some threshold activation is involved (for instance friction). Hence, solutions do include discontinuities/jumps in a natural way. The aim of the thesis would be to investigate the sets of discontinuity for some rate independent problems.
A first step is to show that these rate independent processes can be approximated in a suitable way via processes that react with increasing speed on the environment. This should lead to a concept of solution, which is smooth a.e. The second step would be to investigate the free boundary, which is here the set of discontinuities of the rate independent process. It can be characterized in a natural way as concavity points. |
| References |
| F. Rindler, S. Schwarzacher, E. Suli: Regularity and approximation of strong solutions to rate-independent systems (2017) https://arxiv.org/pdf/1702.01427.pdf
Avner Friedman: Variational Principles and Free-Boundary problems, John Wiley & Sons, Inc. (1982) |