# The monotonicity method for the inverse crack scattering problem

## TL;DR

This paper extends the monotonicity method to inverse crack scattering, providing indicators to determine inclusion relations between unknown cracks and artificial constructs, supported by numerical examples.

## Contribution

It introduces a novel application of the monotonicity method to inverse crack scattering, with new indicators for crack inclusion detection.

## Key findings

- Theorem 1.1 determines if an artificial small arc is within the unknown crack.
- Theorem 1.2 assesses if an artificial large domain contains the unknown crack.
- Numerical examples validate the effectiveness of the proposed indicators.

## Abstract

The monotonicity method for the inverse acoustic scattering problem is to understand the inclusion relation between an unknown object and artificial one by comparing the far field operator with artificial operator. This paper introduces the development of this method to the inverse crack scattering problem. Our aim is to give the following two indicators: One (Theorem 1.1) is to determine whether an artificial small arc is contained in the unknown arc. The other one (Theorem 1.2) is whether an artificial large domain contain the unknown one. Finally, numerical examples based on Theorem 1.1 are given.