Convective Viscous Cahn-Hilliard/Allen-Cahn Equation with memory effects

TL;DR

This work extends the Cahn-Hilliard/Allen-Cahn framework by incorporating convective and viscous terms with memory effects in a one-dimensional setting. It derives an exact traveling-wave solution under memory-augmented diffusion, revealing how the CH and AC dynamics balance against memory and external driving to yield a constant-velocity front. The study identifies precise parametric constraints that must be satisfied for cooperative wave propagation, highlighting regimes where memory enables waves that would be absent otherwise. The results provide analytical insight into surface processes involving adsorption/desorption and diffusion with memory, with implications for phase-field modeling under nonlocal dissipation.

Abstract

The combination of the well-known Cahn-Hilliard and Allen-Cahn equations is used to describe surface processes, such as simultaneous adsorption/desorption and surface diffusion. In the present paper we have considered the convective-viscous Cahn-Hilliard/Allen-Cahn equation complemented by memory effects. Exact solutions are obtained and the combined action of the applied field, dissipation and memory are discussed.