Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A probabilistic view on the long-time behaviour of growth-fragmentation
  semigroups with bounded fragmentation rates   The growth-fragmentation equation models systems of particles that grow and
reproduce as time passes. An important question concerns the asymptotic
behaviour of its solutions. Bertoin and Watson ($2018$) developed a
probabilistic approach relying on the Feynman-Kac formula, that enabled them to
answer to this question for sublinear growth rates. This assumption on the
growth ensures that microscopic particles remain microscopic. In this work, we
go further in the analysis, assuming bounded fragmentations and allowing
arbitrarily small particles to reach macroscopic mass in finite time. We
establish necessary and sufficient conditions on the coefficients of the
equation that ensure Malthusian behaviour with exponential speed of convergence
to the asymptotic profile. Furthermore, we provide an explicit expression of
the latter.

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph