Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Null boundary controllability of a one-dimensional heat equation with an
  internal point mass and variable coefficients   In this paper we consider a linear hybrid system which composed by two
non-homogeneous rods connected by a point mass and generated by the
equation\bea\left\{
  \begin{array}{ll}
  \rho_{1}(x)u_{t}=(\sigma_{1}(x)u_{x})_{x}-q_{1}(x)u,& x\in(-1,0),~t>0,
  \rho_{2}(x)v_{t}=(\sigma_{2}(x)v_{x})_{x}-q_{2}(x)v,& x\in(0,1), ~~~t>0,
  M z_{t}(t)=\sigma_{2}(0)v_{x}(0,t)-\sigma_{1}(0)u_{x}(0,t), &t>0, \end{array}
  \right. \eea with Dirichlet boundary condition on the left end $x=-1$ and a
boundary control acts on the right end $x=1$. We prove that this system is null
controllable with Dirichlet or Neumann boundary controls. Our approach is
mainly based on a detailed spectral analysis together with the moment method.
In particular, we show that the associated spectral gap in both cases
(Dirichlet or Neumann boundary controls) are positive without further
conditions on the coefficients $\rho_{i}$, $\sigma_{i}$ and $q_{i}$ $(i=1,2)$
other than the regularities.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol