Inverse source problem related to one-dimensional Saint-Venant equation

ABSTRACT

The one-dimensional Saint-Venant equation describes unsteady water flow in channels and is derived from the one-dimensional Euler equation by imposing several physical assumptions. In this paper, we consider the linearized and simplified equation in the one-dimensional case featuring a mixed derivative term and prove the global Lipschitz stability of the inverse source problem via the global Carleman estimate.

KEYWORDS:

• Carleman estimate
• inverse source problem
• global Lipschitz stability

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35R30
• 35L20

Acknowledgments

The author would like to thank Professor Masahiro Yamamoto (The University of Tokyo) for many valuable discussions and comments. The author also thank anonymous referees for invaluable comments and Glenn Pennycook, NSc, from Edanz Group (www.edanzediting.com/ac) for editing a draft for this manuscript.

Disclosure statement

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

Additional information

Funding

This work was supported by JSPS and RFBR under the Japan-Russia Research Cooperative Program (project No. J19-721).