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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 15
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Research Article

Asymptotic dynamics of a sixth-order integro-differential equation

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Pages 5537-5556 | Received 23 May 2020, Accepted 27 Feb 2021, Published online: 11 Mar 2021
 

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.

2010 Mathematics Subject Classifications:

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).

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