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arXiv · 1010.4064

Symmetric periodic solutions of parabolic problems with hysteresis

Pavel Gurevich·Sergey Tikhomirov
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Abstract

We consider the heat equation in a multidimensional domain with nonlocal hysteresis feedback control in a boundary condition. Thermostat is our prototype model. We construct all periodic solutions with exactly two switching 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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Pavel Gurevich, Sergey Tikhomirov. 2010-10-19. Symmetric periodic solutions of parabolic problems with hysteresis. https://doi.org/10.1007/s10884-011-9227-0

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