Recovery of the heat equation from a single boundary measurement

Abstract

We prove that we can uniquely recover the coefficient of a one-dimensional heat equation from a single boundary measurement and provide a constructive procedure for its recovery. The algorithm is based on the well-known Gelfand–Levitan–Gasymov inverse spectral theory of Sturm–Liouville operators.

Keywords:

• Heat equation
• inverse spectral problem
• boundary measurement

AMS Subject Classifications:

• 35R30
• 34K29

Acknowledgements

The authors sincerely thank the referees for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.