Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the non existence of non negative solutions to a critical
  Growth-Fragmentation Equation   A growth fragmentation equation with constant dislocation density measure is
considered, in which growth and division rates balance each other. This leads
to a simple example of equation where the so called Malthusian hypothesis
$(M_+)$ of J. Bertoin and A. Watson (2016) is not necessarily satisfied. It is
proved that when that happens, and as it was first suggested by these authors,
no global non negative weak solution, satisfying some boundedness condition on
several of its moments, exist. Non existence of local non negative solutions
satisfying a similar condition, is proved to happen also. When a local non
negative solution exists, the explicit expression is given.

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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: stat
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph