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 2018/2019

12. 6. 2019 (středa!), 11:00 [zasedací místnost ÚMS!]
Prof. Stephen L. Clark (Missouri University of Science and Technology)
Krein's Formula and Sturm-Liouville Operators on a Compact Interval.

Abstrakt
Recalling parametrizations of self-adjoint extensions associated with a regular, symmetric, second-order differential expressions, we give a comprehensive accounting of all self-adjoint extensions of the minimal Sturm–Liouville operator in terms of Krein's formula for resolvent differences given Sturm–Liouville operators with Dirichlet boundary conditions at a and b as a convenient reference operator, and give a detailed description of the Krein extension of the minimal Sturm–Liouville operator.

13. 5. 2019, 12:00 [učebna M5]
dr. Phuoc Tai Nguyen, Ph.D. (Ústav matematiky a statistiky, PřF MU)
Elliptic equations with Hardy potential and gradient-dependent nonlinearity.

Abstrakt
In this talk, I will discuss the boundary value problem with measure data for equation (E) $$- \Delta u - \frac{\mu}{\delta^2}u+ g(|\nabla u|)=0$$ in a smooth bounded domain $$\Omega$$, where $$\mu$$ is a parameter, $$\delta$$ denotes the distance function to $$\partial \Omega$$ and $$g$$ is a continuous, nondecreasing function on $${\mathbb R}_+$$. I will show the existence and uniqueness result. I will also describe the boundary isolated singularities of solutions.
This is a joint work with K. Gkikas.

29. 4. 2019, 12:00 [učebna M5]
Debangana Mukherjee, Ph.D. (Ústav matematiky a statistiky, PřF MU)
Multiplicity results and sign changing solutions of non-local equations with concave-convex nonlinearities.

Abstrakt
In this paper we prove the existence of infinitely many nontrivial solutions of the following equations driven by a nonlocal integro-differential operator $$\mathcal{L}_K$$ with concave-convex nonlinearities and homogeneous Dirichlet boundary conditions \begin{align*} \mathcal{L}_{K} u + \mu\,|u|^{q-1}u + \lambda\,|u|^{p-1}u &\,\,=\,\, 0 \quad\mbox{in}\quad \Omega\\ u&\,\,=\,\,0 \quad\mbox{in}\quad\mathbb{R}^N\setminus\Omega, \end{align*} where $$\Omega$$ is a smooth bounded domain in $$\mathbb{R}^N$$, $$N>2s$$, $$s\in(0,1)$$, $$0 < q < 1 < p\leq\frac{N+2s}{N-2s}$$. Moreover, when $$\mathcal{L}_K$$ reduces to the fractional laplacian operator $$-(-\Delta)^s$$, $$p=\frac{N+2s}{N-2s}$$, $$\frac{1}{2}(\frac{N+2s}{N-2s}) 0$$ such that for any $$\mu\in(0,\mu^*)$$, there exists at least one sign changing solution. This is a joint work with Prof. Mousomi Bhakta.

15. 4. 2019, 12:00 [učebna M5]
doc. Mgr. Petr Hasil, Ph.D. (Ústav matematiky a statistiky, PřF MU)
Difference equations and their oscillation constants.

8. 4. 2019, 12:00 [učebna M5]
Maria Guadalupe Morales Macias, Ph.D. (Ústav matematiky a statistiky, PřF MU)
Fractional-initial value problem.

18. 3. 2019, 12:00 [učebna M5]
Mgr. Peter Šepitka, Ph.D. (Ústav matematiky a statistiky, PřF MU)
New perspectives on the theory of distinguished solutions at infinity of Riccati matrix differential equations.

4. 3. 2019, 12:00 [učebna M5]
Maria Carolina Mesquita (Universidade Federal de São Carlos, Brazílie)
Bifurcation of solutions for generalized ordinary differential equations.

25. 2. 2019, 12:00 [učebna M5]
Prof. Alexandra Rodkina (Univeristy of the West Indies, Jamajka)
Stability shaped by the noise in difference equations.

Abstrakt
An active role of noise perturbations in forming stability properties of solutions of difference equations is explored. Some of our models are inspired by mathematical biology where noise enters naturally through the influence of the environment. We discuss how different types of stochastic perturbations change stability properties of the solution of the deterministic counterpart. We also consider a highly nonlinear stochastic differential equation where stability of the equilibrium is induced by the noise term. It is often challenging to retain such stability in a numerical simulation. We solve this issue by designing an adaptive timestepping discretization scheme which faithfully reproduces stability properties of the solution of the original differential equation.

3. 12. 2018, 12:00 [učebna M5]
doc. RNDr. Michal Veselý, Ph.D. (Ústav matematiky a statistiky, PřF MU)
Critical oscillation case for linear and half-linear equations.

19. 11. 2018, 12:00 [učebna M5]
doc. Andriy Shatyrko, Ph.D. (Taras Shevchenko National University of Kyiv)
Qualitative analysis of Lur’e-type control systems under uncertainties.

5. 11. 2018, 12:00 [učebna M5]
Mgr. Jana Burkotová, Ph.D. (Katedra matematické analýzy a aplikací matematiky, PřF UPOL)
Periodic bouncing solutions of singular second order ODE.

22. 10. 2018, 12:00 [učebna M5]
RNDr. Zdeněk Svoboda, CSc. (Ústav matematiky, FEKT VUT)
Fundamentální matice pro lineární diferenciální systémy s konstantními koeficienty a konstantním zpožděním (habilitační přednáška).

8. 10. 2018, 12:00 [učebna M5]
Maria Guadalupe Morales Macias, Ph.D. (Ústav matematiky a statistiky, PřF MU)
Fractional calculus in the context of Distributional Henstock–Kurzweil integral.

24. 9. 2018, 12:00 [učebna M5]
Dr. Edward Hooton (Matematický ústav AV, Praha)
Hopf bifurcation in equivariant systems; treating non generic scenarios using equivariant topological tools.

Aktualizováno Pátek, 07 Červen 2019 08:02