Identifying an unknown source term of a parabolic equation in Banach spaces

Abstract

A new regularization method for an inverse source problem for a parabolic equation in a Banach space is proposed. Hölder-type error estimates for the regularized solutions are proved for both a priori and a posteriori regularization parameter choice rules. Some numerical examples are presented for illustrating the efficiency of the method.

COMMUNICATED BY:

• M. Klibanov

Keywords:

• Inverse source problems in Banach spaces
• regularization
• error estimates

2010 Mathematics Subject Classifications:

• 35R30
• 35K05

Acknowledgments

We would like to thank the reviewers for their valuable comments and suggestions for greatly improving the quality of the paper. The final version of this work was completed during the stay of Nguyen Van Duc at the Vietnam Institute for Advanced Study in Mathematics (VIASM).

Disclosure statement

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