Citation:
Saci A, Rebiai S-E. An inverse problem for the Schrödinger equation with Neumann boundary condition. Advances in Pure and Applied Mathematics [Internet]. 2023;14 (1) :50-69.
Abstract:
Thisarticleconcernstheinverse problem of the recoveryof unknown potential coefficient for the Schrödinger equation, in a bounded domain of Rn with non-homogeneous Neumann boundary condition from a time-dependent Dirich let 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 aCarleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality. Mathematics Subject Classification. 35R30, 35Q40, 49K20.