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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
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Inequalities for talented pupils of high schools
Šalom, Pavel ; Robová, Jarmila (advisor) ; Boček, Leo (referee)
The thesis contains a textbook for high school pupils. The aim of the textbook is to teach the reader how to solve problems concerning inequalities proposed at czech or international mathematical competitions for high school pupils. In the first part we present some basic ineqaulities (AG, Cauchy's inequality) and we show how to understand them and how to use them. In the second part we broaden reader's horizon by presenting rearrangement and Jensen's inequality. In the third part we present widely applicable methods such as "Abstract Concreteness Method" or "Sum of Squares Method". Some techniques concerning the Sum of Squares Method were written by Phan Kim Hung in 2006. We are trying to significantly involve the reader. We prefer just hints to many of the proposed problems rather than complete solutions and we give some harder problems to solve at the end of each part. 1
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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
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Inequalities for talented pupils of high schools
Šalom, Pavel ; Robová, Jarmila (advisor) ; Boček, Leo (referee)
The thesis contains a textbook for high school pupils. The aim of the textbook is to teach the reader how to solve problems concerning inequalities proposed at czech or international mathematical competitions for high school pupils. In the first part we present some basic ineqaulities (AG, Cauchy's inequality) and we show how to understand them and how to use them. In the second part we broaden reader's horizon by presenting rearrangement and Jensen's inequality. In the third part we present widely applicable methods such as "Abstract Concreteness Method" or "Sum of Squares Method". Some techniques concerning the Sum of Squares Method were written by Phan Kim Hung in 2006. We are trying to significantly involve the reader. We prefer just hints to many of the proposed problems rather than complete solutions and we give some harder problems to solve at the end of each part. 1
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