Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The regularity properties of nonlocal abstract wave equations   In this paper, the regularity properties of Cauchy problem for linear and
nonlinear nonlocal wave equations are studied.The equation involves a
convolution integral operators with a general kernel operator functions whose
Fourier transform are operator functions defined in Hilbert space H together
with some growth conditions. We establish local and global existence and
uniqueness of solutions assuming enough smoothness on the initial data and the
operator functions. By selecting the space H and the operators, the wide class
of wave equations in the field of physics are obtained.

5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con