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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Seminar of Mathematical Physics Equations Group

Weekly research seminar

5070

List of talks

• 2023-02-09, 12:30, 4070

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...

• 2023-01-26, 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, 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, 12:30, 5070

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 terms of the nonlocal nonlinear potential theory. This talk is based ...

• 2022-12-01, 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, 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, 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, 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, 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, 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...