Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A model of morphogen transport in the presence of glypicans III   We analyse a stationary problem for the two dimensional model of morphogen
transport introduced by Hufnagel et al. The model consists of one linear
elliptic PDE posed on $(-1,1)\times(0,h)$ which is coupled via a nonlinear
boundary condition with a nonlinear elliptic PDE posed on $(-1,1)\times\{0\}$.
The main result is that the system has a unique steady state for all ranges of
parameters present in the system. Moreover we consider the problem of the
dimension reduction. After introducing an appropriate scaling in the model we
prove that, as $h\to0$, the stationary solution converges to the unique steady
state of the one dimensional simplification of the model which was analysed in
the first part of the paper. The main difficulty in obtaining appropriate
estimates stems from the presence of a measure source term in the boundary
condition.

6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio