Geodesic
Periodic solutions of parabolic equations with hysteresis in the dimension~1
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 36-54

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We consider the heat equation in the interval with non-ideal relay in the boundary condition. Thermostat is our prototype model. In the most important case of the location of measuring devices near the boundary of the interval we prove existence and stability of unimodal periodic solutions. 
@article{ZNSL_2020_489_a1,
     author = {A. Enin and P. Perstneva and S. Tikhomirov},
     title = {Periodic solutions of parabolic equations with hysteresis in the dimension~1},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {36--54},
     publisher = {mathdoc},
     volume = {489},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a1/}
}
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A. Enin; P. Perstneva; S. Tikhomirov. Periodic solutions of parabolic equations with hysteresis in the dimension~1. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 36-54. http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a1/