Jednadžba porozne sredine

master's thesis

• Author: Josip Žubrinić
• Mentor: Mladen Jurak (mentor)
• Committee member: Mladen Jurak (predsjednik povjerenstva)
• Committee member: Zvonimir Tutek (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome radu smo proučavali jednadžbu porozne sredine, nelinearnu parcijalnu diferencijalnu jednadžbu paraboličkog tipa, koja ima prilično zanimljiva svojstva. U Poglavlju 1 prezentiramo modele u kojima se pojavljuje JPS ili neka njena generalizacija. Nadalje se bavimo njenim specijalnim rješenjima i njihovim svojstvima, izvodimo formule i dokazujemo korisnu propoziciju o graničnom rješenju. U Poglavlju 3 izvodimo apriorne ocjene bitne za daljnji nastavak teorije. U Poglavlju 4 dajemo precizne definicije slabih rješenja homogene Dirichletove zadaće i dokazujemo njihovu egzistenciju i jedinstvenost. U zadnjem poglavlju prezentiramo primjer numeričkog rješenja vezanog uz dvofazni tok u poroznoj sredini.

Abstract (english)

In this thesis we study porous medium equation, nonlinear partial differential equation of parabolic type with some particularly interesting properties. In Chapter 1, we present models involving PME or some of its generalizations. Furthermore, we deal with its special solutions and study their properties, calculate formulas and we give proof to a useful proposition about limit solution. In Chapter 3 we derive a priori bounds crucial for further development of the theory. In Chapter 4 we give precise definitions of weak solutions of homogeneous Dirichlet problem and give proof to their existence and uniqueness. A numerical example related to two-phase flow in porous medium is presented in the last chapter.

• Keywords: jednadžba porozne sredine; nelinearna parcijalna diferencijalna jednadžba paraboličkog tipa; slaba rješenja homogene Dirichletove zadaće; dvofazni tok u poroznoj sredini
• Keywords (english): porous medium equation; nonlinear partial differential equation of parabolic type; weak solutions of homogeneous Dirichlet problem; two-phase flow in porous medium
• Language: croatian
• URN:NBN: urn:nbn:hr:217:164391
• 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: 2019-02-20 15:17:40