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arXiv · 1912.00355

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

Raffaele Folino
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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.

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Raffaele Folino. 2019-12-01. Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension. https://doi.org/10.1016/j.jde.2020.12.024

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