Traveling waves for models of phase transitions of solids driven byconfigurational forces

Shuichi Kawashima; Peicheng Zhu

doi:10.3934/dcdsb.2011.15.309

Article Contents

2011, Volume 15, Issue 1: 309-323. Doi: 10.3934/dcdsb.2011.15.309

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

Shuichi Kawashima^1, and
Peicheng Zhu^2,

1.
Faculty of Mathematics, Kyushu University, Fukuoka 819-0395
2.
Basque Center for Applied Mathematics, Building 500, Bizkaia Technology Park, E-48160 Derio

Received: November 30, 2009

Revised: March 31, 2010

Published: June 2011

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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 transitions of solid materials, e.g., Steel, and phase transitions due to interface motion by interface diffusion, e.g., Sintering. These models were proposed by Alber and Zhu in [3]. 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 transitions in elastic solids.

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Mathematics Subject Classification: Primary: 35D30; 35M13; Secondary: 74N20.

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