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

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

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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
Issue number5
StatePublished - 2012
Externally publishedYes


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


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