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master's thesis
Allen-Cahn jednadžba
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:629916
Čičak, Matea
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Čičak, M. (2017). Allen-Cahn jednadžba (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:629916

Čičak, Matea. "Allen-Cahn jednadžba." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:629916

Čičak, Matea. "Allen-Cahn jednadžba." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:629916

Čičak, M. (2017). 'Allen-Cahn jednadžba', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:629916

Čičak M. Allen-Cahn jednadžba [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:629916

M. Čičak, "Allen-Cahn jednadžba", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:629916

Metadata
TitleAllen-Cahn jednadžba
AuthorMatea Čičak
MentorSiniša Slijepčević (mentor)
Committee memberSiniša Slijepčević (predsjednik povjerenstva)
Committee memberZvonimir Tutek (član povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom smo radu proučavali Allen-Cahnovu jednadžbu, egzistenciju i jedinstvenost njezina rješenja te primjenu. Na početku rada obrađeni su osnovni pojmovi i rezultati koji će se koristiti u nastavku. Definiran je sektorski operator i razlomačke potencije,iskazan teorem o kontrakciji te Gronwallovu nejednakost. U drugom poglavlju smo se bavili paraboličkim diferencijalnim jednadžbama. Dana je bitna teorija egzistencije i jedinstvenosti rješenja tih jednadžbi, čije smo rezultate primjenili na Allen-Cahnovoj jednadžbi. U zadnjem poglavlju opisana je primjena Allen-Cahnove jednadžbe. Proučavali smo bitnu fizikalnu pojavu 'okrupnjavanja'.
Abstract (english)
In this diploma thesis we present Allen-Cahn equation, nonlinear partial differential equation. At the beginning of this paper, we give the basic definitions and notation used throughout the paper. We define sectorial operators and fractional powers, introduce Gronwall’s inequality and contraction mapping theorem. In the Chapter 2 we study the initial-value problem for parabolic partial differential equations. We present theory about uniqueness and existence of the solution and that results apply to the Allen-Cahn equation. In the last Chapter we describe the application of Allen-Cahn equation. We present the physical phenomenon ’coarsening’.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:629916
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-12-21 13:58:49