Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-point boundary value problems and exact controllability for several
  kinds of linear and nonlinear wave equations   In this paper we introduce some new concepts for second-order hyperbolic
equations: two-point boundary value problem, global exact controllability and
exact controllability. For several kinds of important linear and nonlinear wave
equations arising from physics and geometry, we prove the existence of smooth
solutions of the two-point boundary value problems and show the global exact
controllability of these wave equations. In particular, we investigate the
two-point boundary value problem for one-dimensional wave equation defined on a
closed curve and prove the existence of smooth solution which implies the exact
controllability of this kind of wave equation. Furthermore, based on this, we
study the two-point boundary value problems for the wave equation defined on a
strip with Dirichlet or Neumann boundary conditions and show that the equation
still possesses the exact controllability in these cases. Finally, as an
application, we introduce the hyperbolic curvature flow and obtain a result
analogous to the well-known theorem of Gage and Hamilton for the curvature flow
of plane curves.

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat