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

[1] Periodic solutions and asymptotic behavior of a PDE with hysteresis in the source term
Kopfova, Jana
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2006, 36 (02) : 539 - 554
[2] PERIODIC-SOLUTIONS TO A PARABOLIC EQUATION WITH HYSTERESIS
KREJCI, P
MATHEMATISCHE ZEITSCHRIFT, 1987, 194 (01) : 61 - 70
[3] Existence and nonexistence of solutions for the heat equation with a superlinear source term
Fujishima, Yohei
Ioku, Norisuke
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2018, 118 : 128 - 158
[4] SIGN-CHANGING SOLUTIONS OF A QUASILINEAR HEAT EQUATION WITH A SOURCE TERM
Liu, Guirong
Qi, Yuanwei
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (05): : 1389 - 1414
[5] Determination of a source term in a heat equation
Liu, Jinbo
Wang, Baiyu
Liu, Zhenhai
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (05) : 969 - 975
[6] Periodic solutions of a Lienard equation with forcing term
Các, NP
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 43 (03) : 403 - 415
[7] Analytic Solutions of the Cylindrical Heat Equation with a Heat Source
Srivastava, H. M.
Kung, K-Y
Lee, S-F
Lin, S-D
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2021, 28 (04) : 545 - 552
[8] Analytic Solutions of the Cylindrical Heat Equation with a Heat Source
H. M. Srivastava
K.-Y. Kung
S.-F. Lee
S.-D. Lin
Russian Journal of Mathematical Physics, 2021, 28 : 545 - 552
[9] On inverse source term for heat equation with memory term
Duc, Nam Bui
Hai, Nguyen Minh
Hoan, Luu Vu Cam
Long, Le Dinh
DEMONSTRATIO MATHEMATICA, 2024, 57 (01)
[10] Periodic solutions of the Hamilton-Jacobi equation with a periodic forcing term
Sobolevskii, AN
RUSSIAN MATHEMATICAL SURVEYS, 1998, 53 (06) : 1375 - 1376

← 1 2 3 4 5 →