Organizers

prof. dr hab. Grzegorz Łukaszewicz

Information

Thursdays, 12:30 p.m. , room: 5070

Research fields

Mathematical Physics and Applied Analysis

List of talks

Jan. 16, 2020, 12:30 p.m.
Piotr Kokocki (UMK Toruń)
Total integrals of solutions for inhomogeneous Painlevé II equation
We establish a formula determining the value of the Cauchy integrals for the real and purely imaginary Ablowitz-Segur solutions for the inhomogeneous second Painlevé equation. Our approach relies on the Deift-Zhou steepest descent analysis of the corresponding …
Dec. 19, 2019, 12:30 p.m.
dr Maciej Lisicki (Wydzial Fizyki UW)
Pumping and swimming: two faces of phoretic flows
Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. On the other hand, chemically active surfaces can lead to microscale flow generation, bacoming an effective …
Dec. 5, 2019, 12:30 p.m.
Łukasz Chomienia (doktorant MIM)
Energy conservation for the compressible Euler system
We prove the local energy equality for the isentropic compressible Euler equations under the assumption of the Besov regularity in space and the Bochner integrability in time. We show that this result can be established …
Nov. 28, 2019, 12:30 p.m.
Jakub Siemianowski (UMK Toruń)
Systems of elliptic PDEs on R^N
We consider the system of second-order elliptic equations with the nonlinear term depending on the solution and its first-order derivatives on whole R^N. In order to solve it, firstly, we investigate auxiliary systems on large …
Nov. 21, 2019, 12:30 p.m.
Piotr Kalita (UJ)
Rigorous numerical integration of PDEs by means of Finite Element Method
I will present the results on the attractor structure for problems governed by PDEs. I will demonstrate that the approach based on rigorous numerical simulations and Finite Element Method makes it possible to find the …
Nov. 14, 2019, 12:30 p.m.
Grzegorz Łukaszewicz (MIM)
An analogy between electromagnetism and hydrodynamics. Maxwell and Euler equations.
Analogy is a powerful tool of discovery. James Clerk Maxwell, in particular, used certain analogies between hydrodynamics and electromagnetism to better understand the nature of the electromagnetic field. In this talk I shall present …
Nov. 7, 2019, 12:30 p.m.
Cristiana De Filippis (University of Oxford)
Double phase problems
The double phase energy \int_{\Omega} |Dw|^p+a(x) |Dw|^q dx is probably the most extreme example of non-homogeneous structure exhibiting different degeneration rates while simultaneously depending on the space variable. Introduced by V. V. Zhikov in order …
Oct. 24, 2019, 12:30 p.m.
Mikołaj Sierżęga (IMSiM)
On triviality of solutions for a generalised Giga-Kohn equation
Giga-Kohn equation is a particular semilinear elliptic equation of Ornstein-Uhlenbeck type that plays a central role in the description of singularities for the Fujita equation - the semilinear heat equation with power law nonlinearity. In …
Oct. 17, 2019, 12:30 p.m.
Wojciech Szkółka (doktorant Instytutu Geofizyki PAN)
Equatorial Kelvin waves – theory and observations.
The atmosphere is an area of occurrence of phenomena of different spatial scales - from small (about 1mm) to large (about 10 000km). Therefore, different approximations are used to describe its dynamics, depending on the …
Oct. 10, 2019, 12:30 p.m.
Kamila Łyczek (doktorantka MIM)
On differentiability of solutions to the nonlinear transport equation in bounded Radon measures
We consider the nonlinear transport equation in the space of bounded Radon measures. Amongst its applications are structure population model or crowd dynamics. Previous results concerning this type of equations do not allow us to …
Oct. 3, 2019, 12:30 p.m.
Arttu Karppinen (University of Turku, Finlandia)
Regularity of minimizers with generalized Orlicz growth
We will discuss the motivation of studying minimizers of variational integrals or solutions to partial differential equations with generalized Orlicz (also known as Musielak-Orlicz) growth conditions. After introducing the context, a global higher integrability result …
June 13, 2019, 12:30 p.m.
Tomasz Dębiec (doktorant MIM)
On energy conservation in fluid dynamics
Conserved quantities, like the energy, are at the heart of the study of many evolutionary PDEs. We will discuss the problem of energy conservation for some equations of fluid mechanics - starting with the celebrated …
June 6, 2019, 12:30 p.m.
Giuseppe Di Fazio (Università degli Studi di Catania)
Regularity for elliptic equations under minimal assumptions
Elliptic PDEs are ubiquitous in Mathematics and Sciences. A very important topic concerning Elliptic PDEs is the regularity of solutions. We will review some regularity results for linear and quasilinear uniformly elliptic equations. The main focus will be on …
May 30, 2019, 12:30 p.m.
Kamila Łyczek (doktorantka MIM)
Differentiability of measure solutions to the nonlinear transport equation
We consider the nonlinear transport equation in the space of bounded Radon measures. Previous results concerning this type of equation include well-posedness and Lipschitz dependence of the solution (on the initial condition and model ingredients). …
May 23, 2019, 12:30 p.m.
prof. Jacek Szumbarski ( Wydział Mechanicznego Energetyki i Lotnictwa Politechniki Warszawskiej)
Problem warunków brzegowych w modelowaniu przepływów wewnętrznych cieczy newtonowskiej
Tematem referatu jest modelowanie matematyczne i komputerowe niestacjonarnych przepływów cieczy newtonowskiej w układach rozgałęzionych przewodów. Zagadnienia tego typu pojawiają się m.in. w kontekście modelowania układów krwionośnego i oddechowego. Istotnym problemem jest sformułowanie odpowiednich warunków brzegowych …