Determination of a source term in Schr\"odinger equation with a data taken at final moment of observation

TL;DR

This paper proves Lipschitz stability estimates for inverse problems involving the determination of source and zero-order terms in the Schrödinger equation using data collected at the final observation time, under certain conditions.

Contribution

It introduces new Lipschitz stability results for inverse Schrödinger problems with time-dependent coefficients, enhancing understanding of coefficient recovery from final-time data.

Findings

Lipschitz stability estimate for source term determination

Lipschitz stability for zero-order coefficient identification

Results applicable under non-trapping assumptions

Abstract

We establish the Lipshitz stability estimate in inverse problem of determination of a source term or zero order term in the Schr\"odinger equation with time-dependent coefficients under some non-trapping assumption. Based on this result we established the Lipshitz stability of the determination of a real-valued coefficient corresponding to zero-th order term in the Schr\"odinger equation.