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Cotygodniowe seminarium badawcze
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...
2019-03-28, godz. 12:30, 5070
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 a non-weight condition with the mass critical case. Moreover, we sho...
2019-03-21, godz. 12:30, 5070
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 one concerns new phenomena arising in the case...
2019-03-07, godz. 12:30, 5070
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 sphere S2 and investigate how the singular set is affected by small perturbations of the pres...
2019-02-28, godz. 14:15, 5070
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 object. Two problems of this kind will be discussed. First, we will ass...
2018-12-20, godz. 12:30, 5070
Katarzyna Ryszewska (Politechnika Warszawska)
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 the domain of fractional derivative in terms of fraction...
