Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global bifurcation diagram of steady states of systems of PDEs via
  rigorous numerics: a 3-component reaction-diffusion system   In this paper, we use rigorous numerics to compute several global smooth
branches of steady states for a system of three reaction-diffusion PDEs
introduced by Iida et al. [J. Math. Biol., {\bf 53}, 617--641 (2006)] to study
the effect of cross-diffusion in competitive interactions. An explicit and
mathematically rigorous construction of a global bifurcation diagram is done,
except in small neighborhoods of the bifurcations. The proposed method, even
though influenced by the work of van den Berg et al. [Math. Comp., {\bf 79},
1565--1584 (2010)], introduces new analytic estimates, a new {\em gluing-free}
approach for the construction of global smooth branches and provides a detailed
analysis of the choice of the parameters to be made in order to maximize the
chances of performing successfully the computational proofs.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg