Spreading in kinetic reaction–transport equations in higher velocity dimensions
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 vel...
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| Veröffentlicht in: | European journal of applied mathematics 2019-04, Vol.30 (2), p.219-247 |
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| container_title | European journal of applied mathematics |
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| creator | BOUIN, EMERIC CAILLERIE, NILS |
| description | 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. |
| doi_str_mv | 10.1017/S0956792518000037 |
| format | Article |
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| ispartof | European journal of applied mathematics, 2019-04, Vol.30 (2), p.219-247 |
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| language | eng |
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| source | Cambridge University Press Journals Complete |
| subjects | Analysis of PDEs Applied mathematics Mathematics Propagation Transport equations Traveling waves |
| title | Spreading in kinetic reaction–transport equations in higher velocity dimensions |
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