National Repository of Grey Literature 38 records found  1 - 10nextend  jump to record: Search took 0.00 seconds. 
Differential equations with eigenvalue in boundary conditions
Váša, Ondřej ; Kaplický, Petr (advisor) ; Pokorný, Milan (referee)
The goal of this thesis was to study Stokes problem with eigenvalue in bound- ary condition. We were in particular interested in determining the asymptotic be- haviour of the sequence of eigenvalues. We approached this problem by modifying techniques used in several papers studying asymptotic behaviour of eigenvalues in boundary condition for Steklov problem and we wanted to conclude similar re- sults. Firstly, we introduced some theoretical results yielding that the eigenvalue sequence of the problem is corresponding to an eigenvalue sequence of a certain compact and self-adjoint operator. Next, we explicitly calculated precise asymp- totic behaviour of eigenvalues of auxiliary problems on simple domains, however, due to technical difficulties, we were only able to do in two and three dimensions. Finally, by using Min-max Theorem, we managed to get estimates of eigenvalues of the original problem on any bounded C2 domain by eigenvalues of considered auxiliary problems and thus by applying previous results, we managed to prove the desired asymptotic behaviour. 1
Using Version Control Systems to Support Learning
Pokorný, Milan ; Jeřábek, Tomáš (advisor) ; Štípek, Jiří (referee)
The thesis examines version control systems (VCs) and the possibilities of their use in information technology classes. At first, various solutions for version management are evaluated. As a result, a decentralized system called Git is deemed the most appropriate to be used in education. The text further explains the details of how Git works while also introducing some of the relevant training software and Git extensions. The thesis continues by exploring the role of version control systems in education, their teaching, and use as a didactic tool. The final chapters are practically oriented and include the description of processes which allow source code version control to be used within a student group environment. The thesis concludes with an overall evaluation of the use of version management systems in teaching, including practical recommendations and examples.
Matematická analýza regularizovaného modelu viskoelastické nenewtonovské tekutiny
Šalom, Pavel ; Pokorný, Milan (advisor) ; Bulíček, Miroslav (referee)
In this thesis we provide an existence result for a regularized model of viscoelastic non- newtonian fluid. We consider incompressible fluid with shear rate dependent viscosity and with Cauchy stress tensor capable to describe stress relaxation. An elastic part of the Cauchy stress tensor is governed by Oldroyd-type differential equation. In particular, we are interested in fluids with strong shear thinning effect. We prove that if the viscosity function µ (D) is such that tensor µ (D) D is p-coercive, monotone and has (p − 1)-growth for p > 6 5 and some other additional assumptions are satisfied, then there exists a solution to the system of PDEs describing the flow in a bounded domain. The proof is not simple because the convective term is not integrable with a high power. The problem is solved using Lipschitz truncation method for evolution PDEs. 1
Regularity criteria for instationary incompressible Navier-Stokes equations
Axmann, Šimon ; Pokorný, Milan (advisor) ; Neustupa, Jiří (referee)
Title: Regularity criteria for instationary incompressible Navier-Stokes equations Author: Šimon Axmann Institute: Mathematical Institute of Charles University Supervisor: doc. Mgr. Milan Pokorný, Ph.D., Mathematical Institute of Charles University Abstract: In the present thesis we study the global conditional regularity of weak solutions to the Cauchy problem for instationary incompressible Navier-Stokes equations in three space dimensions. In the first section, we present an overview of known conditions implying the full regularity of the equations under conside- ration. For the sake of clarity, we expose only the regularity criteria on the scale of Lebesgue spaces, especially in terms of the velocity and its components, the gradient of the velocity and its components, the pressure and the vorticity. In the subsequent sections, we generalize four regularity criteria using two different techniques. We are able to replace one velocity component or its gradient, consi- dered in the known results, by a projection of the velocity into a general vector field. For the purpose of the second method, we also generalize the multiplicative Gagliardo-Nirenberg inequality.
Fourier method for solving partial differential equations
Tůma, Karel ; Pokorný, Milan (advisor) ; Knobloch, Petr (referee)
Na./cv prace: Fouricrova metoda pro feseni parc.ialnich dirornncialnich rovnic Autor: Karri Tuma Katedra (ust.av): Matematicky ust.av UK Vedouci bakalafske praoo: Mgr. Milan Pokorny, Ph.D. e-mail vodouciho: pokorny@karlin.mff.cuni.cz Abstra.kt: V pfedlo/ene praci odvodime rovnici vedeni tepla a.rovnici slruny. Ty pak nasledno. fesime v jodno prost.orove dimenxi ponioci Fonricrovy me- tody apocivajfci v separaci promennych a nale/eni feseni vc l.varn ncko- nccnc' fady. Zaljyvainc so t.fonii ru/nymi okrajovynii podininkanii. Dah^ vy- sotrujomo vlastnosii foscni tcchlo dvou problcmu. Provadinio analyzu kon- vorgtuicc fx'soni vu tvaru fad v -/avislosti na pocat.ocnich podminkach uloh. Uka/c-me. /o pornoci Fouriorovy inolody l/.c fosil lako stucionarni ulohy, konkrctno so zabyvanio Laplaccoviju rovnici s okrajovynii podminkami na ruznych oblasloch (kruh. vyscc. vyscc mc/ikru/f, mraikru/i). Klicova slova: Parcialni diforoncialni rovnico, Fouricrova tnot.oda, rovnico vodoni lopla, rovnico sLruny. Title: Fourier method for solving partial differential equations Author: Karel Tuma, Department: Matematicky ustav UK Supervisor: Mgr. Milan Pokorny. Ph.D. Supervisor's e-mail address: pokorny@karlin.raff.cuni.cz Abstract: In the present work we derive the heat equation and the wave equation. They arc- solved in one space...
Systems of equations with anizotropic growth of dissipative potential
Kalousek, Martin ; Kaplický, Petr (advisor) ; Pokorný, Milan (referee)
In the present work we study the existence a properties of solution of the system of partial differential equations describing steady flow of Newtonian fluid. We consider that this system has anisotropic dissipative potential. We prove existence of weak solution to this system and its partial C1,α -regularity in 3D and full C1,α -regularity in 2D. 1
Weak formulation of equations describing fluid flows
Dostalík, Mark ; Pokorný, Milan (advisor) ; Kaplický, Petr (referee)
The standard way of deriving the weak formulation of balance equations of continuum mechanics is derived from their localized form, and thus requires differentiability of functions involved in the corresponding balance law. However, the existence of classical solutions of these equations is often not known. It would be suitable to find a transition to the weak formulation of balance laws without the need of their differential form. The aim of this work is to show that the initial integral form of balance equations of continuum mechanics, provided relatively weak assumptions, directly implies their weak formulation, and thus that the weak solution is for these equations a more natural notion than the classical solution is.

National Repository of Grey Literature : 38 records found   1 - 10nextend  jump to record:
See also: similar author names
7 POKORNÝ, Marek
30 POKORNÝ, Martin
1 Pokorný, M.
7 Pokorný, Marek
30 Pokorný, Martin
5 Pokorný, Matyáš
3 Pokorný, Matěj
4 Pokorný, Michael
26 Pokorný, Michal
2 Pokorný, Miroslav
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