caa a22 4500 605515646 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00205-014-0837-7 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0837-7 Propagation in a Kinetic Reaction-Transport Equation: Travelling Waves And Accelerating Fronts [Elektronische Daten] [Emeric Bouin, Vincent Calvez, Grégoire Nadin] In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction term of monostable type. The boundedness of the velocity set appears to be a necessary and sufficient condition for the existence of positive travelling waves. The minimal speed of propagation of waves is obtained from an explicit dispersion relation. We construct the waves using a technique of sub- and supersolutions and prove their weak stability in a weighted L 2 space. In case of an unbounded velocity set, we prove a superlinear spreading. It appears that the rate of spreading depends on the decay at infinity of the velocity distribution. In the case of a Gaussian distribution, we prove that the front spreads as t 3/2. Springer-Verlag Berlin Heidelberg, 2015 Bouin Emeric Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France aut Calvez Vincent Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France aut Nadin Grégoire Université Pierre et Marie Curie-Paris 6, UMR CNRS 7598 ‘LJLL', BC187, 4 place de Jussieu, 75252, Paris cedex 05, France aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/2(2015-08-01), 571-617 0003-9527 217:2<571 2015 217 205 https://doi.org/10.1007/s00205-014-0837-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0837-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bouin Emeric Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France aut NATIONALLICENCE 700 1- Calvez Vincent Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France aut NATIONALLICENCE 700 1- Nadin Grégoire Université Pierre et Marie Curie-Paris 6, UMR CNRS 7598 ‘LJLL', BC187, 4 place de Jussieu, 75252, Paris cedex 05, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/2(2015-08-01), 571-617 0003-9527 217:2<571 2015 217 205