Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time

被引：2

作者：

Al-Nuaimi, Bashar Talib ^{[1
]}

Al-Mahdawi, H. K. ^{[2
]}

Albadran, Zainalabideen ^{[3
]}

Alkattan, Hussein ^{[4
]}

Abotaleb, Mostafa ^{[4
]}

El-kenawy, El-Sayed M. ^{[5
]}

机构：

[1] Univ Diyala, Comp Sci Dept, Diyala 32001, Iraq

[2] Univ Diyala, Elect Comp Ctr, Diyala, Iraq

[3] Univ Alkafeel, Comp Tech Engn Dept, Najaf, Iraq

[4] South Ural State Univ, Dept Syst Programming, Chelyabinsk 454080, Russia

[5] Delta Higher Inst Engn & Technol, Dept Commun & Elect, Mansoura 35111, Egypt

来源：

ALGORITHMS | 2023年 / 16卷 / 01期

关键词：

error estimate; inverse boundary value problem; Fourier transform; ill-posed problem;

D O I：

10.3390/a16010033

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The boundary value problem, BVP, for the PDE heat equation is studied and explained in this article. The problem declaration comprises two intervals; the (0, T) is the first interval and labels the heating of the inside burning chamber, and the second (T, infinity) interval defines the normal cooling of the chamber wall when the chamber temperature concurs with the ambient temperature. It is necessary to prove the boundary function of this problem has its place in the space H-1[0,infinity] in order to successfully apply the Fourier transform method. The applicability of the Fourier transform for time to this problem is verified. The method of projection regularization is used to solve the inverse boundary value problem for the heat equation and to obtain an evaluation for the error between the approximate and the real solution. These results are new and of practical interest as shown in the numerical case study.

引用

页数：14

共 26 条

[1]

Al-mahdawi H. K., 2022, AIP Conference Proceedings, V2398, DOI 10.1063/5.0093361

[2] Parallel multigrid method for solving inverse problems [J].