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Cotygodniowe seminarium badawcze
2023-01-26, godz. 12:30, 5070
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 the flow will be outlined. Another mechanism of bending will be also presented. Exam...
2023-01-19, godz. 12:30, 5070
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 provide analytica...
2022-12-15, godz. 12:30, 5070
Minhyun Kim / Marvin Weidner (Universitaet Bielefeld )
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 terms of the nonlocal nonlinear potential theory. This talk is based ...
2022-12-01, godz. 12:30, 5070
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 and the flow rapidly enters a logarithmic ...
2022-11-24, godz. 12:30, 5070
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 behavior of long slender...
2022-11-03, godz. 12:30, 5070
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 optimal way of moving points from one mass distribution to another in some ...
2022-10-27, godz. 12:30, 5070
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 an array of small holes on the boundary and using the homogenization and the boundary layers, we...
2022-10-20, godz. 12:30, 5070
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 critical points of this energy are difficult to approximate by numerical methods. One ...
2022-10-13, godz. 12:30, 5070
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 may deduce the sharp Harnack estimate. In recent ye...
2022-10-06, godz. 12:30, 5070
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 ...
