Boundary null controllability of convection-diffusion equations with constraints on the state and application to the identification of boundary pollution parameters

Abstract

We study a null controllability problem for a convection-diffusion equation with the control contained in Fourier boundary condition to identify M parameters of pollution. The results are achieved by means of an observability inequality derived from new Carleman estimates for the boundary null controllability and the construction of a boundary sentinel to identify the parameters.

KEYWORDS:

• Carleman inequalities
• null controllability
• sentinel method
• Robin boundary conditions
• Neumann boundary conditions

Acknowledgments

The authors would like to thank the unknown referee for his valuable and accurate comments. These corrections and contributions will significantly improve the quality and the clarity of our work.

Disclosure statement

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