Global bifurcation diagram of steady states of systems of PDEs via rigorous numerics : a 3-component reaction-diffusion system

Auteur(s): Breden, Maxime; Lessard, Jean-Philippe; Vanicat, Matthieu
Résumé: 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. 53(4):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. Comput. 79(271):1565–1584, 2010], introduces new analytic estimates, a new 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.
Date de publication: 22 mars 2013
Date de la mise en libre accès: 18 mai 2016
Version du document: Version of Record
Lien permanent: http://hdl.handle.net/20.500.11794/1388
Ce document a été publié dans: Acta Applicandae Mathematicae, Vol. 128, 113-152 (2013)
http://dx.doi.org/10.1007/s10440-013-9823-6
Springer
Autre version disponible: 10.1007/s10440-013-9823-6
http://arxiv.org/abs/1511.01414
Collection(s) :Articles publiés dans des revues avec comité de lecture

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