Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension

Abstract

In this paper, we consider some hyperbolic variants of the mass conserving Allen-Cahn equation, which is a nonlocal reaction-diffusion equation, introduced (as a simpler alternative to the Cahn-Hilliard equation) to describe phase separation in binary mixtures. In particular, we focus our attention on the metastable dynamics of some solutions to the equation in a bounded interval of the real line with homogeneous Neumann boundary conditions. It is shown that the evolution of profiles with $N+1$ transition layers is very slow and we derive a system of ODEs, which describes the exponentially slow motion of the layers. A comparison with the classical Allen-Cahn and Cahn-Hilliard equations and theirs hyperbolic variations is also performed.

34 pages

References in corpus (5)

• Slow motion for a hyperbolic variation of Allen-Cahn equation in one space dimension
• Metastable dynamics for hyperbolic variations of the Allen-Cahn equation
• Slow dynamics for the hyperbolic Cahn-Hilliard equation in one space dimension
• Metastability and layer dynamics for the hyperbolic relaxation of the Cahn-Hilliard equation
• Analysis and numerics of the propagation speed for hyperbolic reaction-diffusion models