Asymptotic behavior of the solutions to a Landau-Ginzburg system with viscosity for martensitic phase transitions in shape memory alloys
Asymptotic behavior of the solutions to a Landau-Ginzburg system with viscosity for martensitic phase transitions in shape memory alloys
复制标题
形状记忆合金马氏体相变具有粘性的 Landau-Ginzburg 系统解的渐近行为
DOI：
10.1137/s0036141096297698
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发表时间：
1998
影响因子：
2
通讯作者：
P. Zhu
中科院分区：
文献类型：
--
作者：
J. Sprekels;Songmu Zheng;P. Zhu
在本文中，我们研究了在存在（可能很小的）粘性应力的情况下，控制形状记忆合金中马氏体相变动力学的偏微分方程组。相应的自由能假定为朗道—金兹堡形式，并且是非凸的，是序参量的函数。证明了解在时间趋于无穷时的渐近性，并证明了轨道的紧性。
In this paper, we investigate the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a (possibly small) viscous stress. The corresponding free energy is assumed in Landau--Ginzburg form and nonconvex as a function of the order parameter. Results concerning the asymptotic behavior of the solution as time tends to infinity are proved, and the compactness of the orbit is shown.