Determination of a source term in a heat equation

Abstract

This paper investigates the inverse problem of determining an unknown source term in a heat equation subject to the overspecification of the solution at an internal point along with the usual initial boundary conditions, and the source term is only time-dependent. In this paper, the method of trace-type functional formulation of a problem is considered. Some numerical examples using this approach and the finite-difference method are presented and discussed.

Keywords:

• unknown source
• heat equation
• inverse problem
• trace-type functional
• finite-difference method

2000 AMS Subject Classification::

• 35R25
• 35R30
• 49J20

Acknowledgements

The project was supported by NNSF of China Grant No. 10671211 and Hunan Provincial Natural Science Foundation of China Grant No. 07JJ3005.