Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Νικόλαoς Αλικάκος (Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ)
Γεράσιμος Μπαρμπάτης (Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ)
Ιωάννης Στρατής (Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ)
Original Title:
Connecting Orbits for Phase Transition Systems
Translated title:
Connecting Orbits for Phase Transition Systems
Summary:
In this thesis we study solutions of the Allen-Cahn system: -(∆)_xu + (∇_uW(u)) = 0 (1) where W is a double-well potential (in fact W is a nonnegative multiple-well potential but in our considerations the case of exactly two minima of W is particularly significant) . Seeking solutions which are ”heteroclinic” is the main purpose here, beginning with the one-dimensional version of (1) and culminating in its vector version, focusing mostly on the case n = 2. Heteroclinic solutions,or as they called, heteroclinic connections between each pair of minima, in the mathematical theory of phase transitions, describe the behavior of the order parameter across the interface separating the two phases corresponding to the two distinct minima of W.
Main subject category:
Science
Keywords:
Allen-Cahn,energy,heteroclinic connections, minimizers,phase transition systems
File:
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Master Thesis.pdf
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File access is restricted only to the intranet of UoA.
