Traveling waves for models of phase transitions of solids driven by configurational forces

TL;DR

This paper investigates the existence of traveling wave solutions in models of solid phase transitions driven by configurational forces, comparing them with classical diffusion-based models like Allen-Cahn and Cahn-Hilliard.

Contribution

It establishes the existence of traveling wave solutions for recent models of phase transitions driven by configurational forces, including both conserved and non-conserved cases.

Findings

Existence of traveling wave solutions for models of phase transitions.

Comparison with classical diffusion-driven models like Allen-Cahn and Cahn-Hilliard.

Analysis of both diffusionless and interface diffusion-driven phase transformations.

Abstract

This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g., Steel, and phase transitions due to interface motion by interface diffusion, e.g., Sintering. These models are recently proposed by Alber and Zhu. We consider both the order-parameter-conserved case and the non-conserved one, under suitable assumptions. Also we compare our results with the corresponding ones for the Allen-Cahn and the Cahn-Hilliard equations coupled with linear elasticity, which are models for diffusion-dominated phase transformations in elastic solids.