Existence and Continuity of Inertial Manifolds for the Hyperbolic Relaxation of the Viscous Cahn–Hilliard Equation

• Published in: Applied mathematics & optimization Vol. 84; no. 3; pp. 3339 - 3416
• Main Author: Bonfoh, Ahmed
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2021; Springer Nature B.V
• Subjects: Boundary conditions; Calculus of Variations and Optimal Control; Optimization; Control; Convergence; Domains; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical and Computational Physics; Order parameters; Simulation; Smooth boundaries; Spinodal decomposition; Systems Theory; Theoretical; 82C26; 37L25; 35B25; 35B45; Exponential attractors; Inertial manifolds; Continuity; Hyperbolic relaxation; Viscous Cahn–Hilliard equation

We consider the hyperbolic relaxation of the viscous Cahn–Hilliard equation 0.1 ε ϕ tt + ϕ t - Δ ( δ ϕ t - Δ ϕ + g ( ϕ ) ) = 0 , in a bounded domain of R d with smooth boundary when subject to Neumann boundary conditions, and on rectangular domains when subject to periodic boundary conditions. The s...