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Regularity of solutions of systems describing generalized Newtonian fluids
Tichý, Jakub ; Kaplický, Petr (advisor) ; Pokorný, Milan (referee)
We investigate properties of solutions of systems of nonlinear partial differential equations describing evolutionary flow of certain class of generalized Newtonian fluids including in particular various variants of the power-law models. We study the problem with perfect slip boundary conditions. The nonlinear elliptic operator, which is related to the stress tensor, has a p-potential structure. We focus especially on the case p = 2. The main part of the work deals with regularity of second space derivatives and overcoming new di±culties connected with usage of considered boundary conditions.
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The uncertainity principle and the Fourier transform
Ludvík, Pavel ; Kaplický, Petr (referee) ; Pražák, Dalibor (advisor)
Nazev prace: Priucip ueurcitosti ve Fourierove transformaci Autor: Pavel Ludvik Katcdra: Katedra. matematickc analyzy Vcdouci bakalafske prace: RNUr. Dalibor Praza.k, Ph.D. E-mail vedouciho: pra/ak (ikarlin.nifr.cuin.c7 Abstrakt: Mot.iva.ci teto prace je pfedstavem ideje principn ueurcitosti jako obee- nelio matematickeho principu a jeho o/fcjmeni na pfikladech. Zakladem jc dukaz Huist'iiburguvy nerovnosti ]iro ftinkrc1 z AJ (x). Uvddcna json i jcji /cji)ccneni ]>ro fiinkct.1 z /,J{R"), pro obccnrjsi iiorinu a take a.nalogicka uorovnost pro opcratory. Zavcrecna cast prace je vrnovana pfikladmii tzv. kvalitativnich ])rincipu neur- citosti. Xa nirh si niuzcnic vsimnout. ze ideu principn nenrcitosti Ize nalezt v rnzii\'cli odvntvich ina.tenia.liky. Prvni jjfikUvdy vyiizivaji tvr/.cni komplexni a.na- ly/y. kdezto za\'erecna Kohno^orovova vota ma blizko k fnnkcionalni analyze1. Klicova alova: Princi]? ncmfitosti, Fourierova transtbrinaco Title: The uncertainty principle and (lie Fourier transform Author: Pavel Ludvik Department: Dcpartement of niat.heinatical analysis Supervisor: RNDr. Dalibor Prazak. Ph.D. Supervisor's e-mail address: prazakCikarliu.infF.cnni.cz Abstract: The main purpose of this work is introduction of the uncertainty principle a.s the general mathematical idea. We also tried to demonstrate...
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Mathematical Models for Biology
Hruška, Zdeněk ; Pražák, Dalibor (referee) ; Kaplický, Petr (advisor)
Na/.ev pracc: Matematieke modcly v biologii Autor: Zdenek Hruska Katedra: Vedoucf bakalafskc pracc: Mgr. Pctr Kaplicky, Ph.D. e-mail vcdouciho: kaplickyfV/Jkarlin.mff.cuni.cz Abstrakt: Modelovani epidcmii bylo prvnfm / ninoha pfipadu. kdy matematika vstoupila na pole biologic a mediciny. Infckcni cpidemicke ncmoci provazcjf lidstvo od samych pocatku historic a dodnes jsou vclmi zava/nym tcmatem nejen lekafskc vcdy. Ncktere z techto modelu be za velmi specifickych pfedpokladu popsat pomoci soustav obecne nclinearnich diferencialnich rovnic a vysetfovat jcjich kvalitativni vlastnosti jako jc jcjich existence, jednoznacnost a stabilita jcjich feseni. Nektcrc z techto ryzc matematickych vlastnosli systcmu jsou pak velmi blizke vlastnostcm populace realnclio svcta - podstatou modelu je prolo co nejvicc se pfiblizit parametrum skutccnosti, nebol" l/e z nej nejen pro lekafskou praxi vyefst cenne infonnacc. Pfi modelovani cpidcmickych proeesu tedy neni dulezite jen porozumet podslate chorob, ale take pomoci urcit odpovi'dajiei opatfcnf vcctnc oekovaci strategic. Klfcova slova: diferencialni rovnicc, soustavy, biologic Title: Mathematical models in biology Author: /denek Hruska Department: Supervisor: Mgr. Petr Kaplicky, Ph.D. Supervisor's e-mail: kaplickyCoJkarlin.mff.cuni.cz Abstract: The modelling of epidemics...
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