# Non-scattering energies for acoustic-type equations on manifolds with a single flat end

## TL;DR

This paper investigates the existence and lower bounds of non-scattering energies for acoustic equations on manifolds with a flat end, linking the problem to interior transmission eigenvalues.

## Contribution

It establishes a Weyl-type lower bound for the number of non-scattering energies on such manifolds, advancing understanding of wave behavior in inhomogeneous media.

## Key findings

- Proves existence of non-scattering energies under certain conditions
- Derives a Weyl-type lower bound for their count
- Connects non-scattering energies to interior transmission eigenvalues

## Abstract

In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non-scattering energies. Precisely, we show a Weyl-type lower bound for the number of non-scattering energies. Usually a scattered wave occurs for every incident wave by the inhomogeneity of the media. However, there may exist suitable wavenumbers and patterns of incident waves such that the corresponding scattered wave vanishes. We call (the square of) this wavenumber a non-scattering energy in this paper. The problem of non-scattering energies can be reduced to a well-known interior transmission eigenvalues problem.