Note on Boundary Stabilization of Degenerate Schr\"{o}dinger Equations

TL;DR

This paper investigates the boundary stabilization of degenerate Schrödinger equations with fractional damping, establishing polynomial decay rates through resolvent estimates, especially addressing cases with singular damping at boundaries.

Contribution

It introduces a novel analysis of boundary stabilization for degenerate Schrödinger equations with fractional damping, including singular boundary damping cases.

Findings

Polynomial energy decay rates are established.

Resolvent estimates are used to analyze decay.

Boundary damping effects depend on degeneracy type.

Abstract

A degenerate Schr\"{o}dinger equation under fractional integral damping is considered. Here the damping term is singular and not integrable and we consider the two cases when damping acting on the degenerate boundary and nondegenerate boundary. In this paper, we establish polynomial energy decay rates for the degenerate Schr\"{o}dinger equation by using resolvent estimates.