Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity and mass conservation for discrete coagulation-fragmentation
  equations with diffusion   We present a new a-priori estimate for discrete coagulation-fragmentation
systems with size-dependent diffusion within a bounded, regular domain confined
by homogeneous Neumann boundary conditions. Following from a duality argument,
this a-priori estimate provides a global $L^2$ bound on the mass density and
was previously used, for instance, in the context of reaction-diffusion
equations.
  In this paper we demonstrate two lines of applications for such an estimate:
On the one hand, it enables to simplify parts of the known existence theory and
allows to show existence of solutions for generalised models involving
collision-induced, quadratic fragmentation terms for which the previous
existence theory seems difficult to apply. On the other hand and most
prominently, it proves mass conservation (and thus the absence of gelation) for
almost all the coagulation coefficients for which mass conservation is known to
hold true in the space homogeneous case.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol