Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the determination of nonlinear terms appearing in semilinear
  hyperbolic equations   We consider the inverse problem of determining a general nonlinear term
appearing in a semilinear hyperbolic equation on a Riemannian manifold with
boundary $(M,g)$ of dimension $n=2,3$. We prove results of unique recovery of
the nonlinear term $F(t,x,u)$, appearing in the equation
$\partial_t^2u-\Delta_gu+F(t,x,u)=0$ on $(0,T)\times M$ with $T>0$, from some
partial knowledge of the solutions $u$ on the boundary of the time-space
cylindrical manifold $(0,T)\times M$ or on the lateral boundary
$(0,T)\times\partial M$. We determine the expression $F(t,x,u)$ both on the
boundary $x\in\partial M$ and inside the manifold $x\in M$.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex