Uniqueness and stability in the inverse problem of recovering two potential coefficients for coupled Schrödinger equations with Dirichlet conditions

Atef Saci

This paper presents a mathematical analysis of the inverse problem concerning the recovery of two unknown potential coefficients in a coupled Schrödinger equations system, within a bounded domain of the Euclidean space Rn with Dirichlet boundary conditions. Our analysis relies on Neumann boundary measurements, where we establish under a geometric convexity assumption on the interior domain and weak regularity requirements for the data both the uniqueness property and Lipschitz stability for this inverse problem.
The mathematical proof rests on two fundamental pillars: First, the proof of solution uniqueness is based on Carleman estimates specific to Schrödinger equations. Second, the proof of the stability result depends on a combination of (a) the aforementioned uniqueness result, and (b) an observability inequality. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(2) (2026), pp. 181-194