Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr\"odinger Operator with only one Observation

TL;DR

This paper establishes a stability result for simultaneously identifying the diffusion coefficient and potential in a Schrödinger operator within an unbounded strip, using minimal boundary and temporal data.

Contribution

It provides the first stability estimate for jointly recovering two coefficients of a Schrödinger operator with limited boundary observations.

Findings

Proves stability for coefficient identification with one boundary observation

Demonstrates the feasibility of coefficient recovery with minimal data

Extends previous results to unbounded domains

Abstract

This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain.