This article is only in Czech.

Vedoucí semináře:

• Prof. RNDr. Zuzana Došlá, DSc.
  
• Prof. RNDr. Roman Šimon Hilscher, DSc.

Archiv minulých seminářů

Tradiční seminář o diferenciálních rovnicích se koná (obvykle) každé pondělí od 12:00 do 13:30 v zasedací místnosti (první patro ihned naproti schodům) 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 2024/2025

12. 5. 2025 [zasedací místnost ÚMS PřF MU]
od 12:00

dr hab. Agnieszka Malinowska (Katedra matematiky, Technická univerzita v Bělostoku, Polsko)

On Global Exponential Stability of a Switched System Governed by Linear Fractional Difference Equations.

Abstrakt
This lecture addresses the global exponential stability of switched systems described by linear fractional difference equations. Unlike their classical integer-order counterparts, fractional-order systems exhibit memory effects that pose significant challenges for stability analysis. In this talk, I will present a novel framework based on the concept of practical stability, incorporating a fixed memory constraint L. The derived stability conditions utilize the notions of average dwell time and chatter bound to characterize the switching behavior. This approach extends existing methods in the analysis of discrete-time switched fractional systems and offers valuable insights for real-world control engineering applications. The theoretical findings will be supported by numerical examples that illustrate their practical effectiveness.

od 13:00

dr hab. Ewa Girejko (Katedra matematiky, Technická univerzita v Bělostoku, Polsko)

On the stability of memory-dependent multi-agent systems under DoS attacks.

Abstrakt
During the talk, stability analysis of memory-dependent multi-agent systems under Denial-of-Service attacks will be conducted. The system under consideration is of fractional order, involving the Caputo derivative with respect to another function. Necessary and sufficient conditions for the positivity of the fractional linear system will be presented. Moreover, a sufficient condition for asymptotic stability of positive linear fractional switched systems, which is valid for any switching pattern, will be given. Finally, I will present the investigation of the asymptotic stability of multi-agent systems under Denial-of-Service attacks with the use of the results on switched systems. Theoretical considerations will be illustrated by numerical simulations and comparative analyses.

31. 3. 2025, 12:00 [zasedací místnost ÚMS PřF MU]
Seminář věnovaný životnímu jubileu prof. RNDr. M. Bartuška, DSc.

prof. RNDr. Zuzana Došlá, DSc. (Ústav matematiky a statistiky, PřF MU)

Asymptotic properties to higher order fractional differential equations.

17. 3. 2025, 12:00 [zasedací místnost ÚMS PřF MU]

prof. Jan Lang, Dr. (The Ohio State University, USA)

The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings.

Abstrakt
In this lecture, we will explore the eigenvalue problem associated with nonlinear Sobolev embeddings of second order, focusing on the compact inclusion \(W^{2,p}→L^q\) under Navier boundary conditions.
We will discuss the characterization of extremal functions and the role of s-numbers in quantifying the embedding properties. A key result is that the eigenfunctions and eigenvalues exhibit a deep connection to first-order Sobolev embeddings if and only if \(1/p+1/q=1\). In this special case \(q=p′\), we obtain the explicit formulas for the eigenfunctions in terms of generalized trigonometric functions. The lecture will also cover the symmetry, periodicity, and uniqueness properties of solutions, shedding light on the surprising structure of higher-order Sobolev spaces in the \(L^p\) space setting.

3. 3. 2025, 12:00 [zasedací místnost ÚMS PřF MU]

Ing. Tomáš Kisela, PhD. (Ústav matematiky, FSI VUT)

Fractional calculus and its explanation of how stability is lost and found in differential equations (veřejná přednáška v rámci habilitačního řízení).

Online přenos bude vysílán prostřednictvím Zoom na adrese
https://cesnet.zoom.us/j/94712146007?pwd=gA3Uuw3BtYNh9ri6boATq4wy2JAUgk.1
Meeting ID: 947 1214 6007
Passcode: 652422

24. 2. 2025, 12:00 [zasedací místnost ÚMS PřF MU]

prof. Mgr. Pavel Řehák, PhD. (Ústav matematiky, FSI VUT)

Fractional integration and differentiation of asymptotic relations and applications in fractional differential equations.

2. 12. 2024, 12:00 [zasedací místnost ÚMS PřF MU]

doc. Phuoc Tai Nguyen, Ph.D. (Ústav matematiky a statistiky, PřF MU)

Semiclassical Moser–Trudinger inequalities.

Abstrakt
In this talk, I will discuss extensions of the Moser–Trudinger inequality of one function to systems of orthonormal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schrödinger operators on bounded domains.

25. 11. 2024, 12:00 [zasedací místnost ÚMS PřF MU]

doc. RNDr. Antonín Slavík, Ph.D. (Katedra didaktiky matematiky, MFF UK)

New integration rules for Stieltjes integrals and a general form of Gronwall inequality.

11. 11. 2024, 12:00 [zasedací místnost ÚMS PřF MU]

Dr. Sushmita Rawat (Ústav matematiky a statistiky, PřF MU)

Exploring elliptic problems with Choquard nonlinearity.

Abstrakt
In this talk, we investigate the existence of weak solutions for elliptic problems involving Choquard nonlinearity. These equations have attracted significant attention due to their ability to model long-range interactions in various real-world applications. A key concept in solving PDEs is that of weak solutions. These solutions satisfy the integral form of the PDE and are useful when classical solutions may not exist or are challenging to compute. This makes them exceedingly valuable in practical applications. We will use Variational methods to solve the PDEs. This technique essentially transforms the problem of solving a PDE into the problem of finding critical points of the associated functional.

21. 10. 2024, 12:00 [zasedací místnost ÚMS PřF MU]

Ing. Lucie Fedorková (Ústav matematiky, FSI VUT)

Asymptotic and periodic behavior of linear systems of difference equations.

středa (!!) 16. 10. 2024, 16:00 [Aula PřF MU]

doc. RNDr. Michal Veselý, Ph.D. (Ústav matematiky a statistiky, PřF MU)

Non-almost periodic and non-asymptotically almost periodic solutions of difference and differential equations (veřejná přednáška v rámci jmenovacího řízení).

23. 9. 2024, 12:00 [zasedací místnost ÚMS PřF MU]

prof. RNDr. Zuzana Došlá, DSc. (Ústav matematiky a statistiky, PřF MU)

Asymptotic proximity between equations with p-mean curvature operator and with p-Laplacian.