Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of some initial-boundary-value problems for
  dynamo-generated poloidal magnetic fields   Given a bounded domain $G \subset \R^d$, $d\geq 3$, we study smooth solutions
of a linear parabolic equation with non-constant coefficients in $G$, which at
the boundary have to $C^1$-match with some harmonic function in $\R^d \setminus
\ov{G}$ vanishing at spatial infinity.
  This problem arises in the framework of magnetohydrodynamics if certain
dynamo-generated magnetic fields are considered: For example, in the case of
axisymmetry or for non-radial flow fields, the poloidal scalar of the magnetic
field solves the above problem. We first investigate the Poisson problem in $G$
with the above described boundary condition as well as the associated
eigenvalue problem and prove the existence of smooth solutions. As a by-product
we obtain the completeness of the well-known poloidal "free decay modes" in
$\R^3$ if $G$ is a ball. Smooth solutions of the evolution problem are then
obtained by Galerkin approximation based on these eigenfunctions.

31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin