Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral problems for non elliptic symmetric systems with dissipative
  boundary conditions   This paper considers and extends spectral and scattering theory to
dissipative symmetric systems that may have zero speeds and in particular to
strictly dissipative boundary conditions for Maxwell's equations. Consider
symmetric systems $\partial_t - \sum_{j=1}^n A_j \partial_{x_j}$ in ${\mathbb
R}^n,\: n \geq 3$, $n$ odd, in a smooth connected exterior domain $\Omega :=
{\mathbb R}^n \setminus \bar{K}$. Assume that the rank of $A(\xi) = \sum_{j=
1}^n A_j \xi_j$ is constant for $\xi \not= 0.$ For maximally dissipative
boundary conditions on $\Omega :={\mathbb R}^n \setminus \bar{K}$ with bounded
open domain $K$ the solution of the boundary problem in ${\mathbb R}^{+} \times
\Omega$ is described by a contraction semigroup $V(t) = e^{t G_b},\:t \geq 0.$
Assuming coercive conditions for $G_b$ and its adjoint $G_b^*$ on the
complement of their kernels, we prove that the spectrum of $G_b$ in the open
half plane $\Re z < 0$ is formed only by isolated eigenvalues with finite
multiplicities.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph