# Szemináriumok

## Rigid representations of the component structure of dynamic random graph models

Időpont:
2017. 03. 16. 16:15
Hely:
H306
Balázs Ráth (BME)

## Stokes problem, related inequalities, constants and representations

Időpont:
2017. 03. 16. 10:15
Hely:
BME H épület 306-os terem
Zsuppán Sándor (Berzsenyi Dániel Evangélikus Gimnázium (Líceum), Sopron)

Abstract: Stable solvability of the Stokes problem describing fluid motion with small Reynolds number in a domain depends on the inf-sup condition, the discrete version of which is involved in the analysis of many numerical methods. The inf-sup constant figuring in the condition is connected to other domain specific constants figuring in other inequalities such as the Babuska-Aziz inequality for the divergence equation, the Friedrichs-Velte inequality for conjugate harmonic functions and the Korn inequality in linear elasticity. These constants are also connected to the Schur complement operator of the Stokes problem and in the planar case to the Friedrichs operator of the domain. Despite of their theoretical and practical importance exact values of these constants are known only for a few domains. On the other hand there exist useful estimations for planar and spatial domains as well. The values of these constants depend only on the geometry of the domain which is for simply connected planar domains encoded in analytical properties of the conformal mapping of the domain onto the unit disc. Utilization of conformal mapping provides useful results for the constants (exact values or estimations for special domains, and continuous domain dependence) and also for the operators. These results are partly generalizable for other types of domains. We also review some representations of solutions of the Stokes equation by harmonic potentials and formulte results about their equivalence. We also review recent results and outline possible ways for further research of this topic. (The talk will be in Hungarian.)

## Bezdek András 60 éves

Időpont:
2017. 03. 14. 10:30
Hely:
H.306
Hujter Mihály, Lángi Zsolt, G.Horváth Ákos

## Gaussian curvature of piecewise flat manifolds

Időpont:
2017. 03. 09. 10:15
Hely:
H. épület 607-os terem
Snorre Christiansen (University of Oslo)

## Sokaságok és leképezéseik II

Időpont:
2017. 03. 07. 10:30
Hely:
H.306
Kalmár Boldizsár

## Stochastic Arnold Diffusion of Deterministic Systems

Időpont:
2017. 03. 02. 16:15
Hely:
H306
Vadim Kaloshin (U Maryland, ETH Zürich)

## Uniqueness of steady state, smooth shapes in a nonlocal geometric PDE and a model for the shape evolution of ooids

Időpont:
2017. 03. 02. 10:15
Hely:
H306
Sipos András Árpád

We investigate steady state solutions of a nonlocal geometric PDE that serves as a simple model of simultaneous contraction and growth of grains called ooids in geosciences. As a main result of the talk I demonstrate that the parameters associated with the physical environment determine a unique, time-invariant (equilibrium) solution of the equation among smooth, convex curves embedded in $\mathbb{R}^2$. The model produces nontrivial shapes that are consistent with recorded shapes of mature ooids found in nature.

## Uniqueness of steady state, smooth shapes in a nonlocal geometric PDE and a model for the shape evolution of ooids

Időpont:
2017. 03. 02. 10:15
Hely:
BME H épület 306-os terem