Organizatorzy

prof. dr hab. Grzegorz Łukaszewicz

Informacje

czwartki, 12:30 , sala: 5070

Dziedziny badań

Nieliniowe równania różniczkowe cząstkowe w zagadnieniach fizyki i biologii

Lista referatów

10 października 2019 12:30
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 …
3 października 2019 12:30
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 …
13 czerwca 2019 12:30
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 …
6 czerwca 2019 12:30
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 …
30 maja 2019 12:30
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). …
23 maja 2019 12:30
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 …
9 maja 2019 12:30
Panayotis Smyrnelis (IMPAN)
Phase transition and Ginzburg-Landau models occurring in the Physics of liquid crystals.
We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted …
25 kwietnia 2019 12:30
José Carlos Bellido Guerrero (Universidad de Castilla - La Mancha)
A fractional model of hyperelasticity.
Elastic materials are those that deform under the action of an applied force and recover their original configuration when the load stops acting. When the elastic potential energy can be modeled as a variational principle we call …
24 kwietnia 2019 14:15
Adam Prosiński (Oxford University)
Calculus of variations in the anisotropic setting.
In this talk, we will review some recent results concerning existence and regularity of minimizers of anisotropic variational problems. The anisotropy that we have in mind concerns different orders of derivation in different directions, thus …
11 kwietnia 2019 12:30
Michał Łasica (MIM)
Total variation flow of curves in Riemannian manifolds
Let N be a complete Riemannian manifold. We consider the functional of total variation defined on maps from an interval I into N. This is a relaxation with respect to L2 topology on I of …
28 marca 2019 12:30
Hiroshi Wakui (Tohoku University/ Uniwersytet Wrocławski)
Unboundedness for solutions to a degenerate drift-diffusion equation under non-weight condition
In this talk, we consider unboundedness and concentration phenomenon of solutions to a degenerate drift-diffusion equation. We proved that solutions do not remain bounded in time when the initial data has negative free energy under …
21 marca 2019 12:30
Wojciech Górny (doktorant MIM)
Least gradient problem on unbounded domains
We discuss the least gradient problem, which in dimension two is linked to the optimal transport problem, in two settings. The first one concerns the existence of minimisers for discontinuous boundary data, while the second …
7 marca 2019 12:30
Michał Miśkiewicz (doktorant MIM)
Stability of singularities of minimizing harmonic maps
Minimizing harmonic maps - i.e., maps into a fixed manifold that minimize the Dirichlet energy - are known to be smooth outside a singular set of codimension 3. Here, we consider maps into the standard …
28 lutego 2019 14:15
Piotr Szymczak ( IFT UW)
Evolving shapes of dissolving objects in potential flow
If we put a dissolving object in a flow, its shape will continuously change. Tracking of the evolving shape requires the solution of coupled flow and transport equation, in an evolving geometry around the shrinking …
20 grudnia 2018 12:30
Katarzyna Ryszewska (Politechnika Warszawska)
Fractional Calculus
In the talk I will recall definitions of fractional operators and present some of their properties. We will look at the fractional operators in the context of semigroup theory. We will begin with characterization of …