Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovery of time-dependent coefficient on Riemanian manifold for
  hyperbolic equations   Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq
2$, with boundary $\partial M$, we study the inverse boundary value problem of
determining a time-dependent potential $q$, appearing in the wave equation
$\partial_t^2u-\Delta_g u+q(t,x)u=0$ in $\bar M=(0,T)\times M$ with $T>0$.
Under suitable geometric assumptions we prove global unique determination of
$q\in L^\infty(\bar M)$ given the Cauchy data set on the whole boundary
$\partial \bar M$, or on certain subsets of $\partial \bar M$. Our problem can
be seen as an analogue of the Calder\'on problem on the Lorentzian manifold
$(\bar M, dt^2 - g)$.

34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn