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In this paper, we extend and complement previous works about propagation inkinetic reaction-transport equations. The model we study describes particlesmoving according to a velocity-jump process, and proliferating according to areaction term of monostable type. We focus on the case of bounded velocities,having dimension higher than one. We extend previous results obtained by thefirst author with Calvez and Nadin in dimension one. We study the largetime/large scale hyperbolic limit via an Hamilton-Jacobi framework togetherwith the half-relaxed limits method. We deduce spreading results and theexistence of travelling wave solutions. A crucial difference with themono-dimensional case is the resolution of the spectral problem at the edge ofthe front, that yields potential singular velocity distributions. As aconsequence, the minimal speed of propagation may not be determined by a firstorder condition.

Spreading in kinetic reaction-transport equations in higher velocity dimensions