Seminář o diferenciálních rovnicích

Vedoucí semináře:

Tradiční seminář o diferenciálních rovnicích se koná (obvykle) každé pondělí od 12:00 do 13:30 v učebně M5 (přízemí vpravo a na konci chodby opět vpravo) budovy Ústavu matematiky a statistiky (budova č. 8) v areálu Přírodovědecké fakulty (Kotlářská 2). Neobsazené termíny přednášek jsou průběžně doplňovány. V jednání jsou přednášky účastníků našeho semináře a dalších hostů ze zahraničí.

### Program semináře v akademickém roce 2022/2023

5. 12. 2022, 12:00 [posluchárna M5]
prof. RNDr. Roman Šimon Hilscher, DSc. (Ústav matematiky a statistiky, PřF MU)
Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems.

Abstrakt
The talk is based on a joint work with Peter Šepitka. We present an existence result for conjoined bases of nonoscillatory linear Hamiltonian systems on an unbounded interval, which have prescribed numbers of left and right proper focal points. The result is based on a singular Sturmian separation theorem on an unbounded interval by the authors (2019) and it is new even for completely controllable linear Hamiltonian systems, including higher order Sturm-Liouville differential equations. As the main tools we use the comparative index and properties of the minimal principal solution at infinity, which serves as the reference solution for calculating the numbers of proper focal points. We also provide several examples illustrating the presented theory.

21. 11. 2022, 12:00 [posluchárna M5]
Mgr. Jan Jekl (Ústav matematiky a statistiky, PřF MU)
Certain qualitative properties of linear equations on the background of positive solutions.

7. 11. 2022, 12:00 [posluchárna M5]
Thi Minh Thao Le, Ph.D. (Ústav matematiky a statistiky, PřF MU)
Mutiple timescales in microbial interactions.

Abstrakt
We study an epidemiological susceptible-infected-susceptible (SIS) model of multi-strain co-infection, in both non-spatial and spatial frameworks. The infecting agent is structured into $$N$$ strains, which differ according to 5 traits. The resulting system is a large system ($$N^2+N+1$$ equations) whose complete theoretical study is generally inaccessible. This work is therefore based on a simplifying assumption of trait similarity - the so-called quasi-neutrality assumption. It is then possible to implement Tikhonov-type time-scale separation methods. The system is thus decomposed into two simpler subsystems. The first one is a so-called neutral system - i.e., the value of the traits of all the strains are equal - which supports a detailed mathematical analysis and whose dynamics turn out to be quite simple. The second one is a "replication equation" type system that describes the frequency dynamics of the strains and contains all the complexity of the interactions between strains induced by the small variations in the trait values.

24. 10. 2022, 12:00 [posluchárna M5]
prof. RNDr. Miroslav Bartušek, DrSc. (Ústav matematiky a statistiky, PřF MU)
Oscillation of higher order fractional differential equations.

10. 10. 2022, 12:00 [posluchárna M5]
doc. Mgr. Petr Zemánek, Ph.D. (Ústav matematiky a statistiky, PřF MU)
On the principal solution in the Weyl–Titchmarsh theory II.

Aktualizováno Úterý, 22 Listopad 2022 09:28