Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modeling diffusion in thin $2D$-layers separated by a semi-permeable
  membrane   Motivated by models of signaling pathways in B lymphocytes, which have
extremely large nuclei, we study the question of how reaction-diffusion
equations in thin $2D$ domains may be approximated by diffusion equations in
regions of smaller dimensions. In particular, we study how transmission
conditions featuring in the approximating equations become integral parts of
the limit master equation. We device a scheme which, by appropriate rescaling
of coefficients and finding a common reference space for all Feller semigroups
involved, allows deriving the form of the limit equation formally. The results
obtained, expressed as convergence theorems for the Feller semigroups, may also
be interpreted as a weak convergence of underlying stochastic processes.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
1
The categories of this paper are: cs
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph