﻿ Seminář katedry matematiky, Fakulta stavební, ČVUT v Praze

# Seminář katedry matematiky

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 Aktuálně Přednášky Fotogalerie Program

# Seminář katedry matematiky

## Přednášky

Zimní semestr 2017/18

Zde najdete stručný popis již proběhnuvších přednášek.

21. 11. 2017

Název přednášky: Rigorous justification of the asymptotic model describing the nonsteady micropolar pipe flow

Abstrakt: The asymptotic approximation of the nonsteady micropolar fluid flow in a thin (or long) straight pipe is considered. The asymptotic behaviour of the flow is investigated via rigorous asymptotic analysis with respect to the small parameter ϵ, being the ratio between pipe's thickness and its lenght. The corresponding error estimate justifying the obtained asymptotic model is provided.

Reference:
[1] Grigory Panasenko, Konstantin Pileckas, Asymptotic analysis of the nonsteady viscous flow with a given flow rate in a thin pipe, Applicable Analysis: An International Journal, Vol. 91, No. 3, 2012, 559–574
[2] Igor Pažanin, Effective flow of Micropolar Fluid through a Thin or Long Pipe, Mathematical Problems in Engineering, Vol. 2011, (2011) 18 pp.

20. 11. 2017

Název přednášky: On the null-controllability of the semilinear heat equation with hysteresis

Přednášející: Chiara Gavioli

Abstrakt: The null-controllability problem for various kind of linear and semilinear parabolic equations has been an intensively studied subject in the recent years. The main contribution to that was given by Fursikov & Imanuvilov, who introduced (and proved) the so-called Carleman estimates, which have become the major ingredient for obtaining new results. These estimates apply in the linear case, since they arise from the study of the adjoint system.
Given this result, there is a standard technique for getting the null-controllability for the semilinear heat equation: this technique relies on a linearization followed by a fixed-point procedure.
When a some kind of memory is present in the parabolic equation, it is not always clear what is the adjoint system to study in order to obtain, if possible, Carleman estimates. In particular, when the memory term is strongly nonlinear (as hysteresis is), new techniques have to be developed in order to prove null-controllability.
Here an account of such techniques will be given, focusing on the cases in which the hysteresis operator is a Play operator and a Delayed Relay operator.

 Poslední úprava: 22.5.2018 Design stránek: Stanislav Olivík, 2013