Spreading in kinetic reaction-transport equations in higher velocity dimensions
Résumé
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 thanks to a reaction term of monostable type. We focus on the case of bounded velocities, but in dimensions higher than one, the former case being already studied in an earlier paper by the first author with Calvez and Nadin. 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 eigenvectors.
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