On the asymptotic behavior of a phase-field model for elastic phase transitions

被引：0
作者：
Kalies W.D. [1 ]
机构：
[1] Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta
来源：
Journal of Dynamics and Differential Equations | 1997年 / 9卷 / 2期
关键词：
Nonlinear elasticity; Phase transitions; Phase-field model; Wave ringing;
D O I：
10.1007/BF02219224
中图分类号：
学科分类号：
摘要：
We study the asymptotic behavior of a one-dimensional, dynamical model of solid-solid elastic transitions in which the phase is determined by an order parameter. The system is composed of two coupled evolution equations, the mechanical equation of elasticity which is hyperbolic and a parabolic equation in the order parameter. Due to the strong coupling and the lack of smoothing in the hyperbolic equation, the asymptotic behavior of solutions is difficult to determine using standard methods of gradient-like systems. However, we show that under suitable assumptions all solutions approach the equilibrium set weakly, while the phase field stabilizes strongly. © 1997 Plenum Publishing Corporation.
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页码：289 / 306
页数：17
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