Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A construction of two different solutions to an elliptic system   The paper aims at constructing two different solutions to an elliptic system
  $$ u \cdot \nabla u + (-\Delta)^m u = \lambda F
  $$ defined on the two dimensional torus.
  It can be viewed as an elliptic regularization of the stationary Burgers 2D
system.
  A motivation to consider the above system comes from an examination of
unusual propetries of the linear operator
  $\lambda \sin y \partial_x w + (-\Delta)^{m} w$ arising from a linearization
of the equation about the dominant part of $F$.
  We argue that the skew-symmetric part of the operator provides in some sense
a smallness of norms of the linear operator inverse.
  Our analytical proof is valid for a particular force $F$ and for $\lambda >
\lambda_0$, $m> m_0$ sufficiently large. The main steps of the proof concern
finite dimension approximation of the system and concentrate on analysis of
features of large matrices, which resembles standard numerical analysis. Our
analytical results are illustrated by numerical simulations.

1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int