Global weak solutions to a sixth order cahn-hilliard type equation

M. D. Korzec, P. Nayar, P. Rybka

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)3369-3387
Number of pages19
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number5
DOIs
StatePublished - Nov 9 2012

Keywords

  • Cahn-Hilliard type equation
  • Global weak solution
  • Self-assembly

Fingerprint Dive into the research topics of 'Global weak solutions to a sixth order cahn-hilliard type equation'. Together they form a unique fingerprint.

  • Cite this