Stability estimate in an inverse problem for non-autonomous magnetic Schrödinger equations

Abstract

We consider the inverse problem of determining the time-dependent magnetic field of the Schrödinger equation in a bounded open subset of , , from a finite number of Neumann data, when the boundary measurement is taken on an appropriate open subset of the boundary. We prove the Lipschitz stability of the magnetic potential in the Coulomb gauge class by n times changing initial value suitably.

Keywords:

• Schrödinger equation
• time-dependent Hamiltonian
• magnetic vector potential
• inverse problem
• Carleman estimate
• Lipschitz stability estimate

AMS Subject Classifications:

• 65L09
• 65M32

Acknowledgement

The authors are grateful to M. Bellassoued for fruitful discussions concerning this problem and valuable comments.