Organizers

prof. dr hab. Grzegorz Łukaszewicz

Information

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

Research fields

Mathematical Physics and Applied Analysis

List of talks

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 …
Feb. 9, 2023, 12:30 p.m.
Glen Wheeler (University of Wollongong, Australia)
Arbitrarily high order concentration-compactness for curvature flow
We extend Struwe and Kuwert-Schaetzle's concentration-compactness method for analyzing geometric evolution equations to flows of an arbitrarily high order, with the geometric polyharmonic heat flow (GPHF) of surfaces, a generalization of surface diffusion flow, as an exemplar. For the …
Jan. 26, 2023, 12:30 p.m.
Maria Ekiel-Jeżewska (IPPT PAN)
Elastic microfilaments in a shear flow
Dynamical modes of elastic filaments in a shear flow at Reynolds numbers much smaller than unity will be discussed, based on the multipole expansion of the Stokes equations. The role of buckling under compression of …
Jan. 19, 2023, 12:30 p.m.
Sadokat Malikova (SDNŚiP)
Navier-Stokes convergence analysis
We compare different types of obstacle approximation for the steady incompressible Navier-Stokes equations. We compare a standard penalization approximation with approximation by high viscosity in the obstacle region and composition of both methods. For all cases we …
Dec. 15, 2022, 12:30 p.m.
Minhyun Kim / Marvin Weidner (Universitaet Bielefeld )
Wiener criterion for nonlocal Dirichlet problems / Regularity for nonlocal problems with non-standard growth
MK: In this talk, we study the boundary behavior of solutions to the Dirichlet problems for nonlocal nonlinear operators. We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in …
Dec. 1, 2022, 12:30 p.m.
Michał Kowalczyk (Universidad de Chile)
Generation of vortices for the Ginzburg-Landau heat flow.
We consider the Ginzburg-Landau heat flow on the two-dimensional flat torus, starting from an initial data with a finite number of nondegenerate zeros -- but possibly very high initial energy. We show that the initial zeros are conserved …
Nov. 24, 2022, 12:30 p.m.
Philipp Reiter (TU Chemnitz)
Impermeability in nonlinear elasticity models
Maintaining the topology of objects undergoing deformations is a crucial aspect of elasticity models. In this talk we consider two different settings in which impermeability is implemented via regularization by a suitable nonlocal functional. The …
Nov. 3, 2022, 12:30 p.m.
Samer Dweik (MIM UW)
On the regularity of the transport density in the import/export transport problem
The mass transport problem dates back to a work from 1781 by Gaspard Monge (Mémoire sur la théorie des déblais et des remblais) where he formulated a natural question in economics which deals with the …
Oct. 27, 2022, 12:30 p.m.
Prof. Igor Pazanin (Department of Mathematics, Faculty of Science, University of Zagreb, Croatia)
The effective boundary condition on a porous wall
The aim of this talk is to present the derivation of the new effective boundary condition for the fluid flow in a domain with porous boundary. Starting from the Stokes system in a domain with …
Oct. 20, 2022, 12:30 p.m.
Remy Rodiac (Université Paris-Saclay)
On the convergence of critical points of the Ambrosio-Tortorelli functional
In order to describe the behavior of an elastic material undergoing fracture, we can use a variational model and the so-called Mumford-Shah energy defined on a subspace of SBV functions. One difficulty is that the …