Inverse heat source problem from time distributing overdetermination

Abstract

For parabolic equations parametrized by a diffusion coefficient, we consider an inverse problem of finding a source function from a time distributing overdetermining data. We prove that the inverse problem is well-posed in the sense of Hadamard except for a finite set of diffusion parameters. The proof is based on the real analyticity on the parameter and the analytic Fredholm alternative theorem.

Keywords:

• inverse heat source problem
• time distributing observation
• generic well-posedness
• analytic Fredholm theory

Acknowledgements

K. Sakamoto is very grateful to the GCOE Programme and the doctoral course research accomplishment cooperation system at Graduate School of Mathematical Sciences of The University of Tokyo for the support.