Exponentially slow motion of interface layers for the one-dimensional Allen-Cahn equation with nonlinear phase-dependent diffusivity

Raffaele Folino, César Hernández Melo, Luis López Ríos +1

This paper considers a one-dimensional generalized Allen-Cahn equation of the form \[ u_t = \varepsilon^2 (D(u)u_x)_x - f(u), \] where $\epsilon >0$ is constant, $D=D(u)$ is a po…