Stability result for a time dependent potential in a waveguide

TL;DR

This paper establishes a stability result for the time-dependent potential in waveguides using a specialized Carleman estimate, applicable to both bounded and open waveguide geometries with mixed boundary conditions.

Contribution

It introduces a novel stability analysis for time-dependent potentials in waveguides employing an adapted Carleman estimate with singular weights.

Findings

Proves stability for the potential in bounded waveguides with mixed boundary conditions.

Extends stability results to open waveguides with Dirichlet boundary conditions.

Develops a new Carleman estimate tailored for waveguide geometries.

Abstract

We consider the operator $H:= \partial_t -\Delta+V$ in 2D or 3D waveguide. With an adapted global Carleman estimate with singular weight functions we give a stability result for the time dependent part of the potential for this particular geometry. Two cases are considered: the bounded waveguide with mixed Dirichlet and Neumann conditions and the open waveguide with Dirichlet boundary conditions.