Periodic solutions to a heat equation with hysteresis in the source term

Jiashan Zheng; Yuanyuan Ke; Yifu Wang

doi:10.1016/j.camwa.2014.12.002

Periodic solutions to a heat equation with hysteresis in the source term

Jiashan Zheng, Yuanyuan Ke, Yifu Wang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This paper is concerned with a parabolic problem with hysteresis effects in the heat source, which models the feedback control. The existence of periodic solutions is proved by the viscosity approach when the heat force changes periodically in time. More precisely, with the help of the subdifferential operator theory and the Poincaré map, the existence of solutions to the approximation problem is shown and the solution of the periodic problem is obtained under consideration by using a passage-to-limit procedure.

Original language	English
Pages (from-to)	134-143
Number of pages	10
Journal	Computers and Mathematics with Applications
Volume	69
Issue number	2
DOIs	https://doi.org/10.1016/j.camwa.2014.12.002
Publication status	Published - 1 Jan 2015

Keywords

Feedback control
Heat equation
Hysteresis
Periodic solutions

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10.1016/j.camwa.2014.12.002

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Zheng, J., Ke, Y., & Wang, Y. (2015). Periodic solutions to a heat equation with hysteresis in the source term. Computers and Mathematics with Applications, 69(2), 134-143. https://doi.org/10.1016/j.camwa.2014.12.002

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AU - Ke, Yuanyuan

AU - Wang, Yifu

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N2 - This paper is concerned with a parabolic problem with hysteresis effects in the heat source, which models the feedback control. The existence of periodic solutions is proved by the viscosity approach when the heat force changes periodically in time. More precisely, with the help of the subdifferential operator theory and the Poincaré map, the existence of solutions to the approximation problem is shown and the solution of the periodic problem is obtained under consideration by using a passage-to-limit procedure.

AB - This paper is concerned with a parabolic problem with hysteresis effects in the heat source, which models the feedback control. The existence of periodic solutions is proved by the viscosity approach when the heat force changes periodically in time. More precisely, with the help of the subdifferential operator theory and the Poincaré map, the existence of solutions to the approximation problem is shown and the solution of the periodic problem is obtained under consideration by using a passage-to-limit procedure.

KW - Feedback control

KW - Heat equation

KW - Hysteresis

KW - Periodic solutions

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ER -

Periodic solutions to a heat equation with hysteresis in the source term

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Keywords

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