Our aim in this paper is to study the asymptotic behavior, in terms of finite-dimensional attractors, of the sixth-order Cahn-Hilliard system with temperature, namely,

in  subject to the Dirichlet boundary conditions (for simplicity):

and the initial conditions

In this context,  is the order parameter,  is the relative temperature (defined as  where  is the absolute temperature and  is the equilibrium melting temperature),  is the domain occupied by the system  assume here that it is a smooth and bounded domain  , and f is the derivative of a double-well potential  typical choice of the potential is  hence the usual cubic nonlinear term

This system is based on a modification of the Ginzburg-Landau free energy proposed in [1] (see also [9]). In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor.

sixth-order Cahn-Hilliard system with temperature, well-posedness, dissipativity, global attractor, exponential attractor.

Received: March 21, 2024; Accepted: May 10, 2024; Published: October 17, 2024

How to cite this article: Armel Judice Ntsokongo, Narcisse Batangouna and Dieudonné Ampini, On a sixth-order Cahn-Hilliard system with temperature, Far East Journal of Dynamical Systems 37(2) (2024), 205-231. https://doi.org/10.17654/0972111824009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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