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^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	134-143
页数	10
期刊	Computers and Mathematics with Applications
卷	69
期	2
DOI	https://doi.org/10.1016/j.camwa.2014.12.002
出版状态	已出版 - 1 1月 2015

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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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title = "Periodic solutions to a heat equation with hysteresis in the source term",

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 Poincar{\'e} 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.",

keywords = "Feedback control, Heat equation, Hysteresis, Periodic solutions",

author = "Jiashan Zheng and Yuanyuan Ke and Yifu Wang",

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T1 - Periodic solutions to a heat equation with hysteresis in the source term

AU - Zheng, Jiashan

AU - Ke, Yuanyuan

AU - Wang, Yifu

PY - 2015/1/1

Y1 - 2015/1/1

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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DO - 10.1016/j.camwa.2014.12.002

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VL - 69

SP - 134

EP - 143

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2

ER -

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

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