Bressanov problem miješanja

master's thesis

• Author: Marin Tomić
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu proučavamo Bressanov problem miješanja. Dajemo rigoroznu definiciju problema iz Eulerovog i Lagrangeovog gledišta. Prikazujemo rješenje jedne jednodimenzionalne, diskretne varijante problema koju je također formulirao Bressan. Nadalje, prikazujemo pristup dokazu \(L^p\) varijante Bressanove slutnje preko ocjena za bilinearnu singularnu integralnu formu. Na kraju donosimo rješenje još jedne diskretne, dvodimenzionalne varijante problema miješanja.

Abstract (english)

In this thesis we study Bressan’s mixing problem. We give a rigorous formulation of the problem from Eulerian and Lagrangian viewpoints. We present a solution of a one-dimensional, discrete version of the problem formulated by Bressan. We also show an approach to the proof of an \(L^p\) variant of Bressan’s conjecture via boundedness a bilinear singular integral form. Finally, we demonstrate a solution of another, discrete, two-dimensional variant of the mixing problem.

• Keywords: Bressanov problem miješanja; Euler; Lagrange
• Keywords (english): Bressan’s mixing problem; Euler; Lagrange
• Language: croatian
• URN:NBN: urn:nbn:hr:217:506376
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-07-02 11:48:51