Organizers

prof. dr hab. Grzegorz Łukaszewicz

Information

Thursdays, 12:30 p.m. , room: 5070

Research fields

Mathematical Physics and Applied Analysis

List of talks

Oct. 13, 2022, 12:30 p.m.
Mateusz Dembny (doktorant SDNŚiS)
On optimal Harnack bounds for a fractional heat equation
Considering the linear heat equation, the celebrated Li-Yau inequality states that for positive solutions we have $\Delta \log u \geq - \frac{n}{2t}$. By integrating this inequality along a straight space-time interval between two points, we …
Oct. 6, 2022, 12:30 p.m.
Grzegorz Łukaszewicz (MIM UW)
The method of physical analogy
The talk follows my previous one entitled "An analogy between electromagnetism and hydrodynamics" and focuses on some basic features of analogies between mathematical models of physical phenomena, such as partial coincidences, uniqueness of correspondence, classification …
June 9, 2022, 12:30 p.m.
Sadokat Malikova (SDNŚiP)
Approximation of rigid obstacle by highly viscous fluid
This talk is devoted to the problem concerning the approximation of a rigid obstacle for flows governed by the stationary Navier-Stokes equations in the two-dimensional case. The idea is to consider a highly viscous fluid in the …
June 2, 2022, 12:30 p.m.
Maja Szlenk (SDNŚiS)
On the equations modelling certain non-Newtonian compressible fluids
The talk is devoted to the problem of existence of weak solutions to the compressible Stokes system with variable viscosity coefficients. Depending on the form of the stress tensor, different tools are required to deal …
May 26, 2022, 12:30 p.m.
Łukasz Chomienia (SDNŚiP UW)
Higher regularity of weak solutions on low-dimensional structures
The talk is devoted to a regularity of weak solutions of elliptic PDEs on irregular, lowdimensional subsets of the Euclidean space. Due to the singular nature of considered structures and technicalities related to functional spaces, …
May 5, 2022, 12:30 p.m.
Arttu Karppinen (MIM UW )
Stability of solutions to elliptic PDEs under Musielak-Orlicz growth
We investigate stability of solutions to elliptic nonlinear partial differential equations -div(A_i(x,Du))=0 when the growth rate of the differential operator A_i varies. A model example would be to consider solutions of p_i-Laplace equations with p_i …
April 28, 2022, 12:30 p.m.
John Shaw (Department of Geosciences, University of Arkansas)
Necessary conditions for the stability of simple loops
Many self-formed flow networks in nature are loopy, and these loops can occur because of adaptation to fluctuating hydrologic boundary conditions. However, the relationship between fluctuations and loop stability has not been thoroughly tested at …
April 21, 2022, 12:30 p.m.
Tomasz Piasecki (MIM UW)
Stability of the density patches problem with vacuum for incompressible inhomogeneous viscous flows"
The talk will be based on a recent joint work with Piotr B. Mucha and Raphael Danchin. We consider the inhomogeneous incompressible Navier-Stokes system in a smooth two or three dimensional bounded domain, in the …
March 31, 2022, 12:30 p.m.
Prof. Krzysztof Kazimierczuk (Laboratory of NMR Spectroscopy, Centre of New Technologies, University of Warsaw)
NMR spectroscopy as a playground for armchair mathematicians
Nuclear magnetic resonance (NMR) spectroscopy is a branch of chemical analysis, finding applications in material science, structural biology, chemical synthesis, pharma industry, food profiling, medical screening and many other fields. To apply NMR, we need …
March 24, 2022, 12:30 p.m.
Adam Kajzer (IMP PAN Gdańsk)
A weakly compressible, diffuse‑interface model for two‑phase flows
W załączniku. ------------------------------------------------------------------------- Zoom: https://us02web.zoom.us/j/82881783943?pwd=TUp3OGNvZ3R5akpXclZESmx2aGVkUT09
- Streszczenie
March 17, 2022, 12:30 p.m.
Tomasz Dębiec / Bartosz Bieganowski (Sorbonne University / IMPAN)
On incompressible limit for some tissue growth models / Solutions to nonlinear Schroedinger-type problems - recent results and future plans
Abstract (TD): I will discuss some approaches to mathematical modelling of living tissues, with applications to tumour growth. In particular, I will describe recent results related to the incompressible limit of a compressible model which …
March 10, 2022, 12:30 p.m.
Panayotis Smyrnelis ( Basque Center for Applied Mathematics)
Heteroclinic double layers for the vector Allen-Cahn and Fisher-Kolmogorov P.D.E
The first constructions of heteroclinic double layers for the vector Allen-Cahn P.D.E. are due to Alama-Bronsard-Gui (1997), and Schatzman (2002). It is an important result establishing also the existence of two dimensional minimal solutions. I will present …
March 3, 2022, 12:30 p.m.
Iwona Chlebicka (MIM UW)
Potential estimates and local behavior of solutions to nonlinear elliptic equations and systems
We consider measure-data elliptic problems involving a second-order operator in a divergence form exhibiting Orlicz growth and having measurable coefficients. As known in the p-Laplace case, pointwise estimates for solutions expressed with the use of …
Jan. 27, 2022, 12:30 p.m.
Dariusz Wrzosek (MIM UW)
Chemotaxis and pattern formation in predator-prey models
The Rosenzweig-MacArthur predator-prey model, was extended to include the prey's defense mechanism of escaping against the concentration gradient of a chemical signaling the presence of a predator (odor trace). Various variants of the model, which …
Jan. 20, 2022, 12:30 p.m.
Tomasz Cieslak (IMPAN)
Spirale Prandla
Abstract: In my talk, I will review a recent result with P. Kokocki and W.S. Ozanski stating that Prandtl's spirals are weak solutions to the 2d Euler equations. Abstract: In my talk, I will review …