Organizers

prof. dr hab. Grzegorz Łukaszewicz

Information

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

Research fields

Mathematical Physics and Applied Analysis

List of talks

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 …
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 …