Symmetric periodic solutions of parabolic problems with hysteresis

Details Symmetric periodic solutions of parabolic problems with hysteresis Symmetric periodic solutions of parabolic problems with hysteresis

2010-10-19

arxiv.org/abs/1010.4064v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

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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