Some properties of solutions for a sixth-order Cahn–Hilliard type equation with inertial term

ABSTRACT

In this paper, we study a Cahn–Hilliard type equation with inertial term, which arises in dynamics of phase transitions in ternary oil–water–surfactant systems. We use regularity estimates for the semigroups and a classical existence theorem of global attractor to derive that the sixth-order Cahn–Hilliard equation with possesses a global attractor. Using a lemma on the ordinary differential inequality of a second order, we prove the blow-up of the solution for the initial-boundary problem with .

KEYWORDS:

• Sixth order Cahn–Hilliard with inertial term
• attractor
• blow-up

AMS SUBJECT CLASSIFICATIONS:

• 35L25
• 35L35
• 35B44

Acknowledgements

The authors would like to express their deep thanks to the referee’s valuable suggestions for the revision and improvement of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the Jilin Scientific and Technological Development Program [grant number 20170101143JC]; the National Science Foundation of China [grant number 11471164].