Sixth-order Cahn–Hilliard equations with singular nonlinear terms

Abstract

Our aim in this paper is to study the well-posedness for a class of sixth-order Cahn–Hilliard equations with singular nonlinear terms. More precisely, we prove the existence and uniqueness of variational solutions, based on a variational inequality.

Keywords:

• sixth-order Cahn–Hilliard equations
• singular nonlinear terms
• variational solutions
• well-posedness

AMS Subject Classifications:

• 35B45; 35K55

Acknowledgements

The author wishes to thank M. Grasselli and S. Zelik for useful discussions. He also wishes to thank an anonymous referee for her/his careful reading of the paper and useful comments.