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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 1 (January 2023)   > Article

An inverse problem for the Schrödinger equation with Neumann boundary condition

Un problème inverse pour l’opérateur de Schrödinger avec condition au bord de type Neumann


Atef Saci
University of Batna 2
Algeria

Salah-Eddine Rebiai
University of Batna 2
Algeria



Published on 12 January 2023   DOI : 10.21494/ISTE.OP.2023.0906

Abstract

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This article concerns the inverse problem of the recovery of unknown potential coefficient for the Schrödinger equation, in a bounded domain of ℝn with non-homogeneous Neumann boundary condition from a time-dependent Dirichlet boundary measurement. We prove uniqueness and Lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the spatial domain and under weak regularity requirements on the data. The proof is based on a Carleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality.

This article concerns the inverse problem of the recovery of unknown potential coefficient for the Schrödinger equation, in a bounded domain of ℝn with non-homogeneous Neumann boundary condition from a time-dependent Dirichlet boundary measurement. We prove uniqueness and Lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the spatial domain and under weak regularity requirements on the data. The proof is based on a Carleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality.

Inverse problems Uniqueness Stability Schrodinger equations Carleman estimates

Inverse problems Uniqueness Stability Schrodinger equations Carleman estimates