Symmetric Periodic Solutions of Parabolic Problems With Discontinuous Hysteresis

被引：0
作者：
Pavel Gurevich
Sergey Tikhomirov
机构：
[1] Free University of Berlin,Institute for Mathematics I
[2] Pontificia Universidade Catolica do Rio de Janeiro,Departamento de Matematica
来源：
Journal of Dynamics and Differential Equations | 2011年 / 23卷
关键词：
Hysteresis; Parabolic equation; Periodic solution; Stability; Bifurcation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We develop a framework for treating the long-term behavior of solutions for parabolic equations in multidimensional domains with discontinuous hysteresis. Bearing in mind the thermostat model, we concentrate in this paper on the prototype heat equation with hysteresis in the boundary condition. We provide an algorithm for constructing all periodic solutions with exactly two switchings on the period and study their stability. Coexistence of several periodic solutions with different stability properties is proved to be possible. A mechanism of appearance and disappearance of periodic solutions is investigated.
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页码：923 / 960
页数：37
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