# Scattering by the local perturbation of an open periodic waveguide in the half plane

## TL;DR

This paper addresses the scattering problem caused by local perturbations in open periodic waveguides in the half plane, establishing well-posedness under certain conditions using a recently introduced radiation condition.

## Contribution

It extends the application of a new radiation condition to the perturbed case, proving well-posedness for the scattering problem with local perturbations.

## Key findings

- Well-posedness of the perturbed scattering problem established
- Utilizes a recently introduced radiation condition for analysis
- Provides theoretical foundation for waveguide perturbation analysis

## Abstract

We consider the scattering problem of the local perturbation of an open periodic waveguide in the half plane. Recently by Kirsch and Lechleiter, a new radiation condition was introduced in order to solve the unperturbed case. In this paper, with the same radiation condition and an additional assumption we show the well-posedness of the perturbed scattering problem.