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master's thesis
Geometrijske valne jednadžbe
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:010051
Perić, Tomislav
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Perić, T. (2023). Geometrijske valne jednadžbe (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:010051

Perić, Tomislav. "Geometrijske valne jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:010051

Perić, Tomislav. "Geometrijske valne jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:010051

Perić, T. (2023). 'Geometrijske valne jednadžbe', Master's thesis, University of Zagreb, Faculty of Science, accessed 17 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:010051

Perić T. Geometrijske valne jednadžbe [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 May 17] Available at: https://urn.nsk.hr/urn:nbn:hr:217:010051

T. Perić, "Geometrijske valne jednadžbe", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:010051

Metadata
TitleGeometrijske valne jednadžbe
Title (english)Geometric wave equations
AuthorTomislav Perić
MentorNenad Antonić (mentor)
Committee memberNenad Antonić (predsjednik povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
Committee memberMarko Erceg (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu obrađuje se lokalna teorija geometrijskih valnih jednadžbi. Nakon uvođenja osnovnih pojmova i rezultata diferencijalne geometrije s naglaskom na poluriemannove mnogostrukosti, posebno se obrađuju Lorentzove mnogostrukosti. Definiramo pojam linearnog parcijalnog diferencijalnog operatora koji djeluje na glatkim prerezima vektorskog svežnja. Uvodimo pojam normalno hiperboličnog operatora pomoću kojeg definiramo linearnu geometrijsku valnu jednadžbu, kao i pojam distribucije na mnogostrukosti s posebnim naglaskom na Rieszove distribucije pomoću kojih konstruiramo lokalno elementarno rješenje geometrijske valne jednadžbe. Rad zaključujemo dokazom lokalnog postojanja rješenja Cauchyjeve zadaće.
Abstract (english)
This thesis deals with the local theory of geometric wave equations. First, we introduce basic terms and results from differential geometry with an emphasis on semi-Riemannian manifolds. Lorentzian manifolds are treated in particular. Then we define the concept of a linear differential operator that acts on smooth sections of a vector bundle. We introduce the notion of a normally hyperbolic operator, by means of which we define a linear geometric wave equation. Additionally, the notion of distribution on manifolds is introduced with a special emphasis on Riesz distributions, with which we construct the local fundamental solution of the geometric wave equation. Finally, the local existence of the solution to Cauchy’s problem is shown.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:010051
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-02-05 12:27:25