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

Authors: Breden, Maxime; Lessard, Jean-Philippe; Vanicat, Matthieu
Abstract: 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.
Document Type: Article de recherche
Issue Date: 22 March 2013
Open Access Date: 18 May 2016
Document version: VoR
This document was published in: Acta Applicandae Mathematicae, Vol. 128, 113-152 (2013)
Alternative version: 10.1007/s10440-013-9823-6
Collection:Articles publiés dans des revues avec comité de lecture

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