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

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