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 the 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 contains the unknown one. Finally, numerical examples based on Theorem 1.1 are given.

中文翻译：

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逆裂纹散射问题的单调性方法

逆声散射问题的单调性方法是通过比较远场算子和人工算子来理解未知物体和人造物体之间的包含关系。本文介绍了该方法在逆裂纹散​​射问题上的发展。我们的目的是给出以下两个指标： 一（定理1.1）是判断未知弧中是否包含人工小弧。另一个（定理 1.2）是人造大域是否包含未知域。最后，给出了基于定理 1.1 的数值例子。