Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strongly ill-posed problem for a degenerate parabolic equation with
  unbounded coefficients in an unbounded domain $\Omega\times {\mathcal O}$ of
  $\R^{M+N}$   In this paper we deal with a strongly ill-posed second-order degenerate
parabolic problem in the unbounded open set $\Omega\times {\mathcal O}\subset
\mathbb R^{M+N}$, related to a linear equation with unbounded coefficients,
with no initial condition, but endowed with the usual Dirichlet condition on
$(0,T)\times \partial(\Omega\times {\mathcal O})$ and an additional condition
involving the $x$-normal derivative on $\Gamma\times {\mathcal O}$, $\Gamma$
being an open subset of $\Omega$.
  The task of this paper is twofold: determining sufficient conditions on our
data implying the uniqueness of the solution $u$ to the boundary value problem
as well as determining a pair of metrics with respect of which $u$ depends
continuously on the data.
  The results obtained for the parabolic problem are then applied to a similar
problem for a convolution integrodifferential linear parabolic equation.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph