Program v akademickém roce 2023/2024
22. 5. 2024
Jana Hantáková, Milnor, statistical and minimal attractors for generic maps.
15. 5. 2024
Chiara Gavioli (Czech Technical University in Prague), Degenerate diffusion in porous media with hysteresis
Abstract: We propose a model for fluid diffusion in partially saturated porous media taking into account hysteresis effects in the pressure-saturation relation, which are due to surface tension on the liquid-gas interface. The resulting mathematical problem leads to a diffusion equation for the pressure in a bounded N-dimensional domain with a Preisach hysteresis operator under the time derivative. The problem is doubly degenerate in the sense that the saturation range is bounded, and no a priori control of the time derivative of the pressure is available. A convexification argument applied to the hysteresis operator makes it possible to prove the existence and uniqueness of a solution to the problem with standard initial and boundary data. We eventually show that the convexification argument works even if the permeability coefficient depends on the hysteretic saturation. The proof of existence relies on compact anisotropic embeddings in Sobolev and Orlicz spaces, but the problem of uniqueness remains open in this case.
24. 4. 2024
Veronika Rýžová, On one of Birkhoff's theorems and its validity for backward limit sets.
10. 4. 2024
Matěj Moravík, Some unrelated observations concerning proximal dynamic systems.
3. 4. 2024
Jakub Tomaszewski (AGH University of Science and Technology), On the entropy paradox on dendrites.
Abstract: We will examine the values of entropy for mixing dendrite maps in relation to known results for exact and transitive maps. We will construct a pure mixing map of the Gehman dendrite with arbitrarily low entropy.
6. 12. 2023
Veronika Rýžová, Alpha-limit sets,
Michaela Záškolná, $\omega_{\mathcal{N}_T}$-limit sets.
22. 11. 2023
Jana Hantáková, On the Concept of Attractor (John Milnor, Commun. Math. Phys. 99, 177-195 (1985)).
25. 10. 2023
Lenka Rucká, On some open problems concerning non-autonomous systems.
11. 10. 2023
Jana Hantáková, Equicontinuity, transitivity and sensitivity: the Auslander-Yorke dichotomy revisited (Chris Good, Robert Leek, Joel Mitchell).
Seminař se koná zpravidla každý lichý týden ve středu od 13:05 do 14:40 v učebně R1.
