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Spreading in kinetic reaction-transport equations in higher velocity dimensions

Bouin, Emeric; Caillerie, Nils (2019), Spreading in kinetic reaction-transport equations in higher velocity dimensions, European Journal of Applied Mathematics. 10.1017/S0956792518000037

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01518398
Date
2019
Journal name
European Journal of Applied Mathematics
Publication identifier
10.1017/S0956792518000037
Metadata
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Author(s)
Bouin, Emeric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Caillerie, Nils
Institut Camille Jordan [Villeurbanne] [ICJ]
Abstract (EN)
In this paper, we extend and complement previous works about propagation in kinetic reaction-transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction term of monostable type. We focus on the case of bounded velocities, having dimension higher than one. We extend previous results obtained by the first author with Calvez and Nadin in dimension one. We study the large time/large scale hyperbolic limit via an Hamilton-Jacobi framework together with the half-relaxed limits method. We deduce spreading results and the existence of travelling wave solutions. A crucial difference with the mono-dimensional case is the resolution of the spectral problem at the edge of the front, that yields potential singular velocity distributions. As a consequence, the minimal speed of propagation may not be determined by a first order condition.
Subjects / Keywords
travelling waves; Kinetic equations; dispersion relation

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