Unicity of solution for a semi-infinite inverse heat source problem

Abstract

A semi-infinite inverse source problem in heat conduction equations is considered, where the source term is assumed to be compactly supported in the region. After introducing a suitable artificial boundary, the semi-infinite problem is transformed into a bounded one and the corresponding exact expression of the boundary condition is derived. Then we rigorously prove the uniqueness of the solution of original problem, together with the stability of the corresponding optimal control solution.

Keywords

• semi-infinite domain
• heat conduction equation
• inverse source problem
• uniqueness
• stability