Global Weak Solutions to a Sixth Order Cahn--Hilliard Type Equation

Global Weak Solutions to a Sixth Order Cahn--Hilliard Type Equation

We study a sixth order Cahn--Hilliard type equation that arises as a model for the faceting of a growing surface. We show existence of global-in-time weak solutions in two space dimensions, assuming periodic boundary conditions. We also establish exponential-in-time a priori estimates on the $H^3$ n...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:SIAM journal on mathematical analysis 2012-01, Vol.44 (5), p.3369-3387
Hauptverfasser: Korzec, M. D., Nayar, P., Rybka, P.
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Approximation
Boundary conditions
Energy
Quantum dots
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We study a sixth order Cahn--Hilliard type equation that arises as a model for the faceting of a growing surface. We show existence of global-in-time weak solutions in two space dimensions, assuming periodic boundary conditions. We also establish exponential-in-time a priori estimates on the $H^3$ norm of solutions. These bounds enable us to prove the uniqueness of weak solutions. We also show the regularizing effect of the equation on the data. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/100817590