Convergence to generalized transition waves for some Holling-Tanner prey-predator reaction-diffusion system

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.