Title: Spreading in kinetic reaction-transport equations in higher velocity dimensions,
Abstract: 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.