The inverse problem of radiative coefficient for semi-unbounded degenerate parabolic equations

Zhao Yawen; Yang Liu

doi:10.11714/acta.snus.ZR20260021

您当前的位置：

首页 >

文章列表页 >

The inverse problem of radiative coefficient for semi-unbounded degenerate parabolic equations

更新时间：2026-07-13

- The inverse problem of radiative coefficient for semi-unbounded degenerate parabolic equations
- Acta Scientiarum Naturalium Universitatis Sunyatseni Pages: 1-13(2026)
- 作者机构：
  
  兰州交通大学数理学院，甘肃兰州 730070
- 作者简介：
- 基金信息：
- DOI：10.11714/acta.snus.ZR20260021
  CLC： O24
- Revised：2026-06-01，
  
  Accepted：02 June 2026，
  
  Online First：13 July 2026，
- 稿件说明：
移动端阅览
Zhao Yawen, Yang Liu. The inverse problem of radiative coefficient for semi-unbounded degenerate parabolic equations[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-13.
DOI：

Zhao Yawen, Yang Liu. The inverse problem of radiative coefficient for semi-unbounded degenerate parabolic equations[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-13. DOI： 10.11714/acta.snus.ZR20260021.

摘要

系统研究了一类定义在半无界区域上的退化抛物型方程辐射系数反演问题. 首先通过引入精确的人工边界条件，成功将半无界区域上的热传导方程转化为有界区域上的可计算问题；然后基于最优控制框架，将原问题转化为一个优化问题，在对原问题做估计的同时，证明了控制泛函极小值的存在性以及极值所满足的必要条件；随后利用极小元所满足的必要条件证明其唯一性和稳定性. 最后，基于必要条件设计了一种梯度型优化算法，并通过数值算例验证了算法的有效性.

Abstract

A systematic investigation is conducted on the inverse problem of radiative coefficient reconstruction for a class of degenerate parabolic equations defined on semi-unbounded domains. The study begins by introducing an exact artificial boundary condition，which effectively reduces the original problem on the semi-unbounded region to an equivalent formulation on a bounded domain. Within the optimal control framework，the inverse problem is reformulated as a minimization problem. A priori estimates for the direct problem are derived，and the existence of a minimizer for the control functional is established，along with the necessary conditions satisfied by the extremum. The uniqueness and stability of the minimizer are demonstrated through an analysis based on these necessary conditions. Finally，based on the necessary optimality conditions，a gradient-based optimization algorithm was designed，and numerical examples were presented to demonstrate its effectiveness.

关键词

Keywords

references

姜礼尚，陈亚浙，刘西垣，等， 2007 . 数学物理方程讲义［M］. 3版 . 北京：高等教育出版社 .

刘继军， 2005 . 不适定问题的正则化方法及应用［M］. 北京：科学出版社 .

陆金甫，关治， 2004 . 偏微分方程数值解法［M］. 2版 . 北京：清华大学出版社 .

潘坚，王志焕， 2013 . 一类退化抛物型方程解的存在唯一性［J］. 华侨大学学报（自然科学版）， 34 （ 1 ）： 112 - 117 .

杨柳， 2016 . 具奇异或退化性质的二阶抛物型方程的系数反演问题［D］. 兰州：兰州大学 .

Adams R A ， 1981 . 索波列夫空间［M］. 叶其孝，王耀东，应隆安，等，译. 北京：人民教育出版社 .

Dehghan M ， 2001 . An inverse problem of finding a source parameter in a semilinear parabolic equation ［J］. Appl Math Model ， 25 （ 9 ）： 743 - 754 .

Deng Z C ， Yang L ， 2014 . An inverse problem of identifying the radiative coefficient in a degenerate parabolic equation ［J］. Chin Ann Math Ser B ， 35 （ 3 ）： 355 - 382 .

Deng Z C ， Yang L ， 2022 . Unicity of solution for a semi-infinite inverse heat source problem ［J］. AIMS Math ， 7 （ 4 ）： 7026 - 7039 .

Deng Z C ， Yu J N ， Yang L ， 2010 . An inverse problem arisen in the zero-coupon bond pricing ［J］. Nonlinear Anal Real World Appl ， 11 （ 3 ）： 1278 - 1288 .

Egger H ， Engl H W ， 2005 . Tikhonov regularization applied to the inverse problem of option pricing： Convergence analysis and rates ［J］. Inverse Probl ， 21 （ 3 ）： 1027 - 1045 .

Ismailov M I ， Oğur B ， 2016 . An inverse diffusion problem with nonlocal boundary conditions ［J］. Numerical Methods Partial Differential Eq ， 32 （ 2 ）： 564 - 590 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

TwoLevel Optimal Control Method and its Theory Analysis for Central AirConditioning System

Well-posedness for a Free Boundary Problem Modeling Protocells

The Study on EqualityRenew Method for Twolevel Optimal Control of Central AirConditioning System

Balanced Exponential Growth for a Size-structured Two-phase Population Model with Delayed Birth Process

Kirchhoff indices of Cayley graphs on T4n×ℤm

Related Author

NIE Yuqiang

BAI Meng

CUI Shangbin

KUANG Xiaolei

BAI Meng

FENG Zhaoyong

XU Shihe

Related Institution

Foshan Architectural Design Institute

School of Mathematics and Computational Science, Sun Yatsen University

Foshan Construction Project Institute

School of Mathematics and Information Sciences, Zhaoqing University



Postal code：510275
Tel：020-84112585，84113223 Email：xuebaozr@mail.sysu.edu.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备09064830号-19 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰