Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On vanishing and localizing of transmission eigenfunctions near singular
  points: a numerical study   This paper is concerned with the intrinsic geometric structure of interior
transmission eigenfunctions arising in wave scattering theory. We numerically
show that the aforementioned geometric structure can be much delicate and
intriguing. The major findings can be roughly summarized as follows. If there
is a cusp on the support of the underlying potential function, then the
interior transmission eigenfunction vanishes near the cusp if its interior
angle is less than $\pi$, whereas the interior transmission eigenfunction
localizes near the cusp if its interior angle is bigger than $\pi$.
Furthermore, we show that the vanishing and blowup orders are inversely
proportional to the interior angle of the cusp: the sharper the angle, the
higher the convergence order. Our results are first of its type in the spectral
theory for transmission eigenvalue problems, and the existing studies in the
literature concentrate more on the intrinsic properties of the transmission
eigenvalues instead of the transmission eigenfunctions. Due to the limitedness
of the computing resources, our study is by no means exclusive and complete. We
consider our study only in a certain geometric setup including corner, curved
corner and edge singularities. Nevertheless, we believe that similar results
hold for more general cusp singularities and rigorous theoretical
justifications are much desirable. Our study enriches the spectral theory for
transmission eigenvalue problems. We also discuss its implication to inverse
scattering theory.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg