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Cotygodniowe seminarium badawcze
2019-11-28, godz. 12:30, 5070
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 balls B_n. Then, by suitable estimates and the so-called tail est...
2019-11-21, godz. 12:30, 5070
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 trajectories in the global attractor. As an example I will present the proof of...
2019-11-14, godz. 12:30, 5070
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 a formal analogy between Euler equations expressed in n...
2019-11-07, godz. 12:30, 5070
Cristiana De Filippis (University of Oxford)
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 to study homogeneization problems ...
2019-10-24, godz. 12:30, 5070
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 the 80' Giga and Kohn provided a key 'triviali...
2019-10-17, godz. 12:30, 5070
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 nature of the phenomena we are interested in. From the model typical for ...
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 ...
