Organizers

prof. dr hab. Grzegorz Łukaszewicz

Information

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

Research fields

Mathematical Physics and Applied Analysis

List of talks

Jan. 11, 2024, 12:30 p.m.
Antoine Detaille (Université Claude-Bernard-Lyon-I)
Strong density in Sobolev spaces to manifolds
In striking contrast with what happens to classical Sobolev spaces, the space of smooth maps with values into a compact manifold $N$ does not need to be dense in the space of $N$-valued $W^{s,p}$ maps. …
Nov. 30, 2023, 12:30 p.m.
Michał Fabisiak (doktorant SDNŚiS)
Cucker-Smale model in bounded domains
Cucker-Smale model describes the behaviour of agents aligning their velocities according to nonlocal protocol. We consider the model posed in domains with a boundary and try to justify the mean-field limit between particle and kinetic …
Nov. 23, 2023, 12:30 p.m.
Mateusz Dembny (doktorant SDNŚiS)
On differential Harnack bounds for a fractional heat equation
Consider the linear heat equation. The celebrated Li-Yau inequality states that for positive solutions we have $\bigtriangleup \log u \geq - \frac{n}{2t}$. By integrating this inequality along a straight space-time interval between two points, we …
Nov. 9, 2023, 12:30 p.m.
Łukasz Chomienia (SDNŚiP)
PDEs on low-dimensional structures: regularity and parabolic issues
By the low-dimensional structure we understand a closed subset of Euclidean space possessing some geometrical nature. The class includes, for instance, CW-complexes, families of manifolds, stratified manifolds etc. We very briefly recall the current state …
Oct. 26, 2023, 12:30 p.m.
Jarosław Duda (Institute of Computer Science and Computer Mathematics, Jagiellonian University)
Electromagnetism with built-in electric charge quantization as topological
I will discuss topological solitons starting with 1+1 dimensional sine-Gordon model. Then I will consider higher dimensional model, like topological defects with long-range e.g. Coulomb-like interactions observed in liquid crystals. To recreate electromagnetism for them …
Oct. 19, 2023, 12:30 p.m.
Benoît Van Vaerenbergh (UCLouvain)
The p-harmonic relaxation versus the Ginzburg-Landau functional
We will describe the manifold-valued harmonic extension problem of a boundary data defined on the boundary of a domain and taking values into the manifold. This extension has engineering applications, which we will present. Unfortunately, …
June 1, 2023, 12:30 p.m.
Martin Ostoja-Starzewski (University of Illinois at Urbana-Champaign, USA)
Tensor Random Fields
See attached file
- Abstract
May 25, 2023, 12:30 p.m.
Benjamin Lledos (Université Paul Sabatier, Institut de Mathématiques de Toulouse)
Some results about the uniqueness of the solutions in the calculus of variations
We want to find a framework in which we can establish the uniqueness of solutions for non-strictly convex problems in the calculus of variations. The main idea is to extend a method devised by Marcellini …
May 18, 2023, 12:30 p.m.
Mateusz Dembny (SDNŚiS)
Spiral vortex sheets and 2d Euler equation
In my talk, I will introduce Prandtl's and Kaden's spirals. Prandtl's spirals are weak solutions to the 2d Euler equation and this is a result by T. Cieslak, P. Kokocki and W.S. Ozanski. We will check whether Kaden's …
May 4, 2023, 12:30 p.m.
Michał Borowski (MIMUW)
Absence of Lavrentiev’s phenomenon and Musielak-Orlicz-Sobolev spaces
We want to study Lavrentiev’s phenomenon for a broad class of variational functionals, covering anisotropic functionals of non-standard growth. To this purpose, we consider Musielak–Orlicz–Sobolev spaces and describe how the density of regular functions guarantees …
April 13, 2023, 12:30 p.m.
Michał Fabisiak (doktorant SDNŚiS)
Monokineticity and mean-field limit for strongly singular Cucker-Smale model
Cucker-Smale model, introduced in 2007, describes the evolution of particles alligning their velocities according to nonlocal interaction protocol. We will focus on the strongly singular case and see that, under some mild assumptions, measure valued …
March 30, 2023, 12:30 p.m.
Maja Szlenk (SDNŚiS)
A multifluid model with chemically reacting components – construction of weak solutions.
We investigate the existence of weak solutions to the multi-component system, consisting of compressible chemically reacting components, coupled with the Stokes equation for the velocity. Specifically, we consider the case of irreversible chemical reaction and …
March 23, 2023, 12:30 p.m.
Markus Schmidtchen (TU Dresden)
A degenerate cross-diffusion system as the inviscid limit of a nonlocal tissue growth model.
In recent years, there has been a spike in the interest in multi-phase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law, Brinkman's law or …
March 9, 2023, 2:30 p.m.
Iwona Chlebicka (IMSIM )
Approximation in the calculus of variations
Typical techniques of proving regularity of minimizers to variational functionals are based on a construction of a sequence of nice solutions to auxiliary problems, that is convergent in a relevant way. If the growth of …
March 2, 2023, 12:30 p.m.
Stanisław Żukowski (IFT FUW UW)
Through history to growth dynamics: deciphering the evolution of spatial networks.
Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for …