Year: 2024
Type: article
Abstract: 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 (we assume here that it is a smooth and bounded domain ), and is the derivative of a double-well potential (a 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.
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4403491286