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Cotygodniowe seminarium badawcze
2020-01-23, godz. 12:30, 5070
Wojciech Górny (doktorant MIM)
Structure of solutions to the least gradient problem
In the least gradient problem with discontinuous boundary data, the solutions may fail to be unique. However, they often share a similar structure. In this talk, I will discuss the geometrical reasons for this phenomenon, with a particular focus on anisotropic cases. ...
2020-01-16, godz. 12:30, 5070
Piotr Kokocki (UMK Toruń)
Total integrals of solutions for inhomogeneous Painlevé II equation
We establish a formula determining the value of the Cauchy integrals for the real and purely imaginary Ablowitz-Segur solutions for the inhomogeneous second Painlevé equation. Our approach relies on the Deift-Zhou steepest descent analysis of the corresponding Riemann-Hilbert proble...
2019-12-19, godz. 12:30, 5070
dr Maciej Lisicki (Wydzial Fizyki UW)
Pumping and swimming: two faces of phoretic flows
Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. On the other hand, chemically active surfaces can lead to microscale flow generation, bacoming an effective pumping mechanism in inertia-less small-scale flow...
2019-12-05, godz. 12:30, 5070
Łukasz Chomienia (doktorant MIM)
Energy conservation for the compressible Euler system
We prove the local energy equality for the isentropic compressible Euler equations under the assumption of the Besov regularity in space and the Bochner integrability in time. We show that this result can be established in a certain class of exponents determining the regularity. We also use t...
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 ...
