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Cotygodniowe seminarium badawcze
2019-10-10, godz. 12:30, 5070
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 get the differentiability of solutions with respect to a perturbation ...
2019-10-03, godz. 12:30, 5070
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 ...
2019-06-13, godz. 12:30, 5070
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 Onsager's conjecture in the realm of i...
2019-06-06, godz. 12:30, 5070
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 the ...
2019-05-30, godz. 12:30, 5070
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). However, these results do not allow to analyze the ...
2019-05-23, godz. 12:30, 5070
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 pro...
2019-05-09, godz. 12:30, 5070
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 by the model. In particular we show existence of a new type of topological...
2019-04-25, godz. 12:30, 5070
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 then hyperplastic materials, and it is the nat...
2019-04-24, godz. 14:15, 4050
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 we work with differential operators that need not be ho...
2019-04-11, godz. 12:30, 5070
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 the length functional defined on parametrized curves. We investigate well-posedness of the steepest descent fl...
