Determination of a spacewise-dependent heat source by a logarithmic-type regularization method

Abstract

This paper is devoted to an inverse problem of determining a spacewise-dependent heat source in a linear parabolic equation from the measurement at the final moment. A new regularization method called the logarithmic-type regularization method is proposed to determine the unknown source. Then the convergence estimates of regularization solutions are obtained under the a-priori and a-posteriori regularization parameter selections. Finally, some numerical examples are presented to verify the validity of the logarithmic-type regularization method.

Keywords:

• Inverse source problem
• parabolic equation
• logarithmic-type regularization method

2020 Mathematics Subject Classifications:

• 35R30
• 35R11
• 65M32

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundation of China (11961002,12171248), the key project of Jiangxi Provincial Natural Science Foundation (20212ACB201001).