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

被引：3

作者：

Zheng, Jiashan ^{[1
]}

Ke, Yuanyuan ^{[2
]}

Wang, Yifu ^{[1
]}

机构：

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[2] Renmin Univ China, Sch Informat, Beijing 100872, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2015年 / 69卷 / 02期

关键词：

Heat equation; Feedback control; Hysteresis; Periodic solutions; PARABOLIC PROBLEMS; MODEL; PDES;

D O I：

10.1016/j.camwa.2014.12.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 Poincare 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. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：134 / 143

页数：10

共 50 条

[41] On Qualitative Behaviour of Solutions to a Thin Film Equation with a Source Term
M. Chugunova
Y. Ruan
R. Taranets
Journal of Nonlinear Science, 2021, 31
[42] Numerical Methods for Determining the Coefficient and the Source Term in the Heat Equation
Denisov A.M.
Solov’eva S.I.
Computational Mathematics and Modeling, 2022, 33 (4) : 389 - 400
[43] ON THE IDENTIFICATION OF SOURCE TERM IN THE HEAT EQUATION FROM SPARSE DATA
Rundell, William
Zhang, Zhidong
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2020, 52 (02) : 1526 - 1548
[44] Recovering Source Term and Temperature Distribution for Nonlocal Heat Equation
Ilyas, Asim
Malik, Salman A.
Saif, Summaya
APPLIED MATHEMATICS AND COMPUTATION, 2023, 439
[45] Numerical method of identification of an unknown source term in a heat equation
Fatullayev, AG
MATHEMATICAL PROBLEMS IN ENGINEERING, 2002, 8 (02) : 161 - 168
[46] Asymptotic behaviour to a heat equation with a delayed control in the source term
Berrone, L
Mannucci, P
CONTROL AND CYBERNETICS, 2004, 33 (01): : 5 - 32
[47] On the controllability of the semilinear heat equation with hysteresis
Bagagiolo, Fabio
PHYSICA B-CONDENSED MATTER, 2012, 407 (09) : 1401 - 1403
[48] Blow up, exponential decay of solutions for a G-heat equation with source term: Analytical and numerical results
Ouaoua, Amar
Boughamsa, Wissem
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2025, 43
[49] Self-similar solutions for the heat equation with a positive non-Lipschitz continuous, semilinear source term
Farina, A.
Gianni, R.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2024, 79
[50] On Natural Continua of Periodic Solutions of the Systems with Hysteresis
D. I. Rachinskii
Automation and Remote Control, 2003, 64 : 420 - 438

← 1 2 3 4 5 →