Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conservative parabolic problems: non-degenerated theory and degenerated
  examples from population dynamics   We consider partial differential equations (PDE) of drift-diffusion type in
the unit interval, supplemented by either two conservation laws or by a
conservation law and a further boundary condition. We treat two different
cases: (i) uniform parabolic problems; (ii) degenerated problems at the
boundaries. The former can be treated in a very general and complete way, much
as the traditional boundary value problems. The latter, however, bring new
issues, and we restrict our study to a class of forward Kolmogorov equations
that arise naturally when the corresponding stochastic process has either one
or two absorbing boundaries. These equations are treated by means of a uniform
parabolic regularisation, which then yields a measure solution in the vanishing
regularisation limit that is unique. Two prototypical problems from population
dynamics are treated in detail.

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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: econ
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org