2009/12/21 by Shuichi Kawashima, Kawashima, Shuichi, Peicheng Zhu +1
Computer Science · Engineering · Materials Science · Mathematics · #35J #35K #74N #Advanced Mathematical Modeling in Engineering #Aluminum Alloy Microstructure Properties #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Solidification and crystal growth phenomena #math.AP #math.DS #msc:35J #msc:35K #msc:74N
paper · pdf · doi:10.48550/arxiv.0912.4146
16 pages, 1 figure
arxiv created 2009/12/21 · openalex publication_date 2009/12/21 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.