An inverse problem of finding a time-dependent parameter in a bilinear heat equation

被引：0

作者：

El Mezegueldy, Redouane ^{[1
]}

Ouakrim, Youssef ^{[1
]}

Ouzahra, Mohamed ^{[1
]}

机构：

[1] Univ Sidi Mohamed Ben Abdellah, Ecole Normale Super, MASI Lab, Fes, Morocco

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2025年

关键词：

Reaction-diffusion equation; inverse problem; time-dependent control; bilinear control; thresholding algorithm; PARABOLIC EQUATION; CONTROLLABILITY; COEFFICIENT;

D O I：

10.1515/jiip-2022-0080

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the inverse problem of estimating an unknown bilinear control u, applied locally in a reaction-diffusion equation. Our goal is to achieve a temperature profile close to a desired reference at the final time. We formulate the problem as an optimal control framework and analyze the existence, optimality conditions and stability of the solution with respect to the data. An algorithm and some numerical experiments are proposed to show the effectiveness of our approach in steering the system towards a desired state.

引用

页数：20

共 50 条

[1] An inverse time-dependent source problem for the heat equation
Hazanee, A.
Ismailov, M. I.
Lesnic, D.
Kerimov, N. B.
APPLIED NUMERICAL MATHEMATICS, 2013, 69 : 13 - 33
[2] An inverse problem of finding a time-dependent coefficient in a fractional diffusion equation
Durdiev, Durdimurod
Durdiev, Dilshod
TURKISH JOURNAL OF MATHEMATICS, 2023, 47 (05) : 1437 - 1452
[3] The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data
Kanca, Fatma
Ismailov, Mansur I.
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2012, 20 (04) : 463 - 476
[4] AN INVERSE PROBLEM OF FINDING A PARAMETER IN A SEMILINEAR HEAT-EQUATION
CANNON, JR
LIN, YP
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1990, 145 (02) : 470 - 484
[5] Finding a time-dependent reaction coefficient of a nonlinear heat source in an inverse heat conduction problem
Rashedi, Kamal
JOURNAL OF MATHEMATICAL MODELING, 2024, 12 (01): : 17 - 32
[6] On an initial inverse problem in nonlinear heat equation associated with time-dependent coefficient
Tuan Nguyen Huy
APPLICATIONS OF MATHEMATICS, 2014, 59 (04) : 453 - 472
[7] On an initial inverse problem in nonlinear heat equation associated with time-dependent coefficient
Tuan Nguyen Huy
Applications of Mathematics, 2014, 59 : 453 - 472
[8] Inverse heat problem of determining time-dependent source parameter in reproducing kernel space
Wang, Wenyan
Han, Bo
Yamamoto, Masahiro
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (01) : 875 - 887
[9] Regularization for the Inverse Problem of Finding the Purely Time-Dependent Volatility
Trong D.D.
Thanh D.N.
Lan N.N.
Vietnam Journal of Mathematics, 2016, 44 (3) : 513 - 530
[10] An inverse problem for the linear Boltzmann equation with a time-dependent coefficient
Bellassoued, Mourad
Boughanja, Yosra
INVERSE PROBLEMS, 2019, 35 (08)

← 1 2 3 4 5 →