Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 100, Issue 1, Pages 1-15Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
DOI: 10.1016/j.matpur.2012.10.009
Keywords
Generalized transition waves; Long time behaviour; Prey-predator system
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This manuscript is devoted to the study of some spreading properties of Holling-Tanner prey-predator reaction-diffusion system. We more particularly focus on the invasion of introduced predator in some environment which is initially well-populated of prey. We first prove that, for the arbitrary dimensional problem, the system has a spreading speed property. We derive more precise information for the one-dimensional system for which the long time behaviour is studied and it is proved that the solution converges (in some sense) towards a generalized transition wave with some determined global mean speed of propagation. (c) 2012 Elsevier Masson SAS. All rights reserved.
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