Κατεύθυνση Εφαρμοσμένα Μαθηματικά
Library of the School of Science

2017-07-14

2017

Vamvakas Nikolaos

Αλικάκος Νικόλαος , Καθηγητής ,Τμήμα Μαθηματικών Ε.Κ.Π.Α (επιβλέπων) [ nalikako@math.uoa.gr]
Μπαρμπάτης Γεράσιμος ,Αναπληρωτής, Τμήμα Μαθηματικών Ε.Κ.Π.Α [ gbarbatis@math.uoa.gr]
Στρατής Ιωάννης, Καθηγητής, Τμήμα Μαθηματικών Ε.Κ.Π.Α [ istratis@math.uoa.gr]

Το Στάσιμο Κύμα για Ελλειπτικά Συστήματα Αλλαγής Φάσης

Greek

The Standing wave for Elliptic Systems of Phase Transition

In this work,we study and construct solutions of elliptic system Δu-W_u(u)=0,where Δ is a Laplacian operator.Moreover we still interest how these solutions are described in phase plane.We will see in scalar case (m=1, u:R->R) we have heteroclinic connections which connect the minimal of potential W.In addition, we prove that the variational problem has a solution in the lip of cylinder and with minimal energy(minimizer).While in the end of Chapter 2 we prove the existense of (unique) connection via characterization of minimal solutions of system.In chapter 3 it grows the method of Noether for stress-energy tensor T. The tensor has two useful properties :divT=0 [divergence free condition] and the other concerns the trace it.These properties have an application to the following:Monotonicity formula,Modica estimate,Hamiltonian identities and Liouville Theorem.Finally,we present the Maximal Principle and cut-off lemma for the class of solutions u of the Euler-Lagrange equation of the functional of energy.

Science

Analysis

Functional of Energy,solutions of Euler-Lagrange,Heteroclinic connections,minimizers,stress-energy tensor,monotonicity formula,phase transition,Modica estimate,cut-off lemma

No

0

Yes

14

56

File access is restricted only to the intranet of UoA.

https://pergamos.lib.uoa.gr/uoa/dl/object/1720823