Work

Uniqueness for the Schrödinger equation with an inverse square potential and application to controllability and inverse problems

Year: 2024

Type: article

Abstract: In this paper, we prove a sharp uniqueness result for the singular Schrödinger equation with an inverse square potential. This will be done without assuming geometrical restrictions on the observation region. The proof relies on a recent technique transforming the Schrödinger equation into an elliptic equation. We show that this technique is still applicable for singular equations. In our case, substantial difficulties arise when dealing with singular potentials of cylindrical type. Using the uniqueness result, we show the approximate controllability of the equation using a distributed control. The uniqueness result is also applied to prove the uniqueness for an inverse source problem.

Source: Evolution equations and control theory

DOI: 10.3934/eect.2024063

Author: Salah-Eddine Chorfi

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404075690

FWCI: 0.158

Cites: 29

Cited by: 1

Related to: 10