Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The monotonicity method for the inverse crack scattering problem   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.

3
The categories of this paper are: physics
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom