Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High frequency analysis of Helmholtz equations: case of two point
  sources   We derive the high frequency limit of the Helmholtz equation with source term
when the source is the sum of two point sources. We study it in terms of Wigner
measures (quadratic observables). We prove that the Wigner measure associated
with the solution satisfies a Liouville equation with, as source term, the sum
of the source terms that would be created by each of the two point sources
taken separately. The first step, and main difficulty, in our study is the
obtention of uniform estimates on the solution. Then, from these bounds, we
derive the source term in the Liouville equation together with the radiation
condition at infinity satisfied by the Wigner measure.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex