Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic analysis of a selection model with space   Selection of a phenotypical trait can be described in mathematical terms by
'stage structured' equations which are usually written under the form of
integral equations so as to express competition for resource between
individuals whatever is their trait. The solutions exhibit a concentration
effect (selection of the fittest); when a small parameter is introduced they
converge to a Dirac mass. An additional space variable can be considered in
order to take into account local environmental conditions. Here we assume this
environment is a single nutrient which diffuses in the domain. In this
framework, we prove that the solution converges to a Dirac mass in the
physiological trait which depends on time and on the location in space with
Lipschitz continuity. The main difficulties come from the lack of compactness
in time and trait variables. Strong convergence can be recovered from
uniqueness in the limiting constrained equation after Hopf-Cole change of
unknown. Our analysis is motivated by a model of tumor growth introduced by
Lorz et al. (preprint) in order to explain emergence of resistance to therapy.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga