Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Papalazarou Alexia
Supervisors info:
Νικόλαος Αλικάκος, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
The Cahn-Hilliard equation-Construction of a periodic solution
Translated title:
The Cahn-Hilliard equation-Construction of a periodic solution
Summary:
This thesis is devoted to the Cahn-Hilliard (CH) equation. Cahn-Hilliard, belongs in a class of evolution equations of reaction-diffusion type.
From a physical point of view: We deal with a phase change problem where interfaces are created.
CH equation conserves mass and reduces the Energy functional.
At geometric level: Cahn-Hilliard conserves the volume enclosed and the reduces the perimeter.
We are interested in constructing a class of solutions which are not simple, sphere-like but instead are periodic, unbounded Constant Mean Curvature surface-like.
Method:
First Approximation: The 1-d heteroclinic solution
Second Approximation: Expansion of 1-d solution near a CMC surface (Key Pieces: ODE’s theory, Phase plane analysis)
Expansion to the whole space (Key Pieces: Definition of a non-linear operator through CH, the linearisation of this operator, Lyapounov-Schmidt reduction, fixed point argument)
Main subject category:
Science
Keywords:
Cahn, Hilliard, solution, periodic
