Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness for a hyperbolic inverse problem with angular control on the
  coefficients   Suppose $q_i(x)$, $i=1,2$ are smooth functions on $\R^3$ and $U_i(x,t)$ the
solutions of the initial value problem {gather*} \pa_t^2 U_i- \Delta U_i -
q_i(x) U_i = \delta(x,t), \qquad (x,t) \in \R^3 \times \R U_i(x,t) =0, \qquad
\text{for} ~ t<0. {gather*} Pick $R,T$ so that $0 < R < T$ and let $C$ be the
vertical cylinder $\{(x,t) \, : |x|=R, ~ R \leq t \leq T \}$. We show that if
$(U_1, U_{1r}) = (U_2, U_{2r})$ on $C$ then $q_1 = q_2$ on the annular region
$R \leq |x| \leq (R+T)/2$ provided there is a $\gamma>0$, independent of $r$,
so that \[\int_{|x|=r} | \Delta_S (q_1 - q_2)|^2 \, dS_x \leq \gamma
\int_{|x|=r} |q_1 - q_2|^2 \, dS_x, \qquad \forall r \in [R, (R+T)/2].\] Here
$\Delta_S$ is the spherical Laplacian on $|x|=r$.

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The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an