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Symmetric periodic solutions of parabolic problems with hysteresis. / Gurevich, P.; Tikhomirov, S.

In: Journal of Dynamics and Differential Equations, Vol. 23, No. 4, 2011, p. 923-960.

Research output: Contribution to journal › Article

Harvard

Gurevich, P & Tikhomirov, S 2011, 'Symmetric periodic solutions of parabolic problems with hysteresis', Journal of Dynamics and Differential Equations, vol. 23, no. 4, pp. 923-960. https://doi.org/10.1007/s10884-011-9227-0

APA

Gurevich, P., & Tikhomirov, S. (2011). Symmetric periodic solutions of parabolic problems with hysteresis. Journal of Dynamics and Differential Equations, 23(4), 923-960. https://doi.org/10.1007/s10884-011-9227-0

Vancouver

Gurevich P, Tikhomirov S. Symmetric periodic solutions of parabolic problems with hysteresis. Journal of Dynamics and Differential Equations. 2011;23(4):923-960. https://doi.org/10.1007/s10884-011-9227-0

Author

Gurevich, P. ; Tikhomirov, S. / Symmetric periodic solutions of parabolic problems with hysteresis. In: Journal of Dynamics and Differential Equations. 2011 ; Vol. 23, No. 4. pp. 923-960.

BibTeX

@article{f801d60e92064b27ac33587c5b6faad6,
title = "Symmetric periodic solutions of parabolic problems with hysteresis",
abstract = "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.",
author = "P. Gurevich and S. Tikhomirov",
year = "2011",
doi = "10.1007/s10884-011-9227-0",
language = "не определен",
volume = "23",
pages = "923--960",
journal = "Journal of Dynamics and Differential Equations",
issn = "1040-7294",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Symmetric periodic solutions of parabolic problems with hysteresis

AU - Gurevich, P.

AU - Tikhomirov, S.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

U2 - 10.1007/s10884-011-9227-0

DO - 10.1007/s10884-011-9227-0

M3 - статья

VL - 23

SP - 923

EP - 960

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 4

ER -

ID: 5467231