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Existence of pulses for a monotone reaction-diffusion system

Martine Marion 1, 2 Vitaly Volpert 3, 2
2 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We consider a monotone reaction-diffusion system of the form w 1 − w1 + f1(w2) = 0, w 2 − w2 + f2(w1) = 0, and address the question of the existence of pulses, that is of positive decaying at infinity solutions. We prove that pulses exist if and only if the wave speed of the associated travelling-wave problem is positive. The proofs are based on the Leray-Schauder method which uses topological degree for elliptic problems in unbounded domains and a priori estimates of solutions in weighted spaces.
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Submitted on : Tuesday, November 15, 2016 - 9:32:57 AM
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Martine Marion, Vitaly Volpert. Existence of pulses for a monotone reaction-diffusion system. Pure and Applied Functional Analysis, Yokohama Publishers, 2016. ⟨hal-01396839⟩

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