Propagation in a Kinetic Reaction-Transport Equation: Travelling Waves And Accelerating Fronts
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0837-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0837-7 | ||
| 245 | 0 | 0 | |a Propagation in a Kinetic Reaction-Transport Equation: Travelling Waves And Accelerating Fronts |h [Elektronische Daten] |c [Emeric Bouin, Vincent Calvez, Grégoire Nadin] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Bouin |D Emeric |u Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France |4 aut | |
| 700 | 1 | |a Calvez |D Vincent |u Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France |4 aut | |
| 700 | 1 | |a Nadin |D Grégoire |u Université Pierre et Marie Curie-Paris 6, UMR CNRS 7598 ‘LJLL', BC187, 4 place de Jussieu, 75252, Paris cedex 05, France |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/2(2015-08-01), 571-617 |x 0003-9527 |q 217:2<571 |1 2015 |2 217 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0837-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0837-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bouin |D Emeric |u Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Calvez |D Vincent |u Ecole Normale Supérieure de Lyon, UMR CNRS 5669 ‘UMPA', and INRIA Alpes, project-team NUMED, 46 allée d'Italie, 69364, Lyon cedex 07, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Nadin |D Grégoire |u Université Pierre et Marie Curie-Paris 6, UMR CNRS 7598 ‘LJLL', BC187, 4 place de Jussieu, 75252, Paris cedex 05, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/2(2015-08-01), 571-617 |x 0003-9527 |q 217:2<571 |1 2015 |2 217 |o 205 | ||