A modified quasi-boundary value method for solving the radially symmetric inverse heat conduction problem

Abstract

In this paper, we consider a radially symmetric inverse heat conduction problem of determining the surface heat flux distribution from a fixed location inside a cylinder. This problem is ill-posed in the Hadamard sense and a conditional stability estimate is given for it. A modified quasi-boundary value regularization method is applied to formulate a regularized solution, and a sharp error estimate between the approximate solution and the exact solution is established by choosing a suitable regularization parameter. A numerical example is presented to verify the efficiency of the regularization method.

Keywords:

• Ill-posed problem
• radially symmetric inverse heat conduction
• quasi-boundary value method
• error estimate
• surface heat flux

AMS Subject Classifications:

• 65M30
• 35R25
• 35R30

Acknowledgements

The authors would like to thanks the editor and the anonmous referees for their valuable comments and suggestions that improve the quality of our paper.

Additional information

Funding

The work is supported by the National Natural Science Foundation of China [grant number 11171136], [grant number 11561045]; the Natural Science Foundation of Henan Province of China [grant number 132300410231].