Compacton formation under Allen--Cahn dynamics

Abstract

We study the solutions of a generalized Allen-Cahn equation deduced from a Landau energy functional, endowed with a non-constant higher order stiffness. We analytically solve the stationary problem and deduce the existence of so-called compactons, namely, connections on a finite interval between the two phases. The dynamics problem is numerically solved and compacton formation is described.

References in corpus (6)

• Theory of Phase Ordering Kinetics
• Allen-Cahn and Cahn-Hilliard-like equations for dissipative dynamics of saturated porous media
• Phase-field model of long-time glass-like relaxation in binary fluid mixtures
• Soft and hard wall in a stochastic reaction diffusion equation
• Phase coexistence in consolidating porous media
• Kink Localization under Asymmetric Double-Well Potential

Cited by in corpus (3)

• Exponentially slow motion of interface layers for the one-dimensional Allen-Cahn equation with nonlinear phase-dependent diffusivity
• Long-time behavior of solutions to the generalized Allen-Cahn model with degenerate diffusivity
• Stability of the stationary solutions of the Allen-Cahn equation with non-constant stiffness