Identifying temperature distribution and source term for generalized diffusion equation with arbitrary memory kernel

被引：4

作者：

Ilyas, Asim ^{[1
]}

Khalid, Rooh A. ^{[1
]}

Malik, Salman A. ^{[1
]}

机构：

[1] COMSATS Univ Islamabad, Dept Math, Pk Rd, Islamabad, Pakistan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 07期

关键词：

bi-orthogonal system of functions; generalized diffusion equation; inverse problem; Mittag-Leffler-type functions; Riesz basis; INVERSE SOURCE PROBLEM; FRACTIONAL DIFFUSION; UNIQUENESS; FAMILY;

D O I：

10.1002/mma.9896

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A diffusion equation involving integral convolution in time variable with arbitrary kernel and nonlocal boundary conditions is considered. The existence and uniqueness results for two inverse problems of determining source terms (space- and time-dependent sources) along with diffusion concentration from appropriate over-specified conditions are presented. A bi-orthogonal system of functions is used to have series representation of the solutions of the inverse problems. Several special cases such as standard diffusion, multi-term diffusion, and tempered diffusion equations are discussed, and some examples are provided.

引用

页码：5894 / 5915

页数：22

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