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Abstract
We consider a sixth-order integro-differential equation with periodic boundary conditions. The equation describes the phase transition dynamics in ternary oil–water–surfactant systems. Using the energy methods and the basic dissipative estimate, we establish the required estimates. Furthermore, based on these estimates, we prove the existence of the attractors by a decomposition of the solution semigroup.
Acknowledgments
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 author(s).