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Cotygodniowe seminarium badawcze
Organizatorzy
- prof. dr hab. Grzegorz Łukaszewicz
Informacje
czwartki, 12:30 , sala: 5070Dziedziny badań
Lista referatów
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28 listopada 2019 12:30
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 …
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21 listopada 2019 12:30
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 …
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14 listopada 2019 12:30
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 …
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7 listopada 2019 12:30
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 …
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24 października 2019 12:30
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 …
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17 października 2019 12:30
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 …
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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 …
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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 …
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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 …
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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 …
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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). …
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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 …
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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 …
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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 …
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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 …
