Fast propagation for KPP equations with slowly decaying initial conditions |
| |
Authors: | François Hamel Lionel Roques |
| |
Institution: | a Aix-Marseille Université & Institut Universitaire de France, LATP, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20, France b UR 546 Biostatistique et Processus Spatiaux, INRA, F-84000 Avignon, France |
| |
Abstract: | This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the unstable steady state more slowly than any exponentially decaying function. We prove that all level sets of the solutions move infinitely fast as time goes to infinity. The locations of the level sets are expressed in terms of the decay of the initial condition. Furthermore, the spatial profiles of the solutions become asymptotically uniformly flat at large time. This paper contains the first systematic study of the large-time behavior of solutions of KPP equations with slowly decaying initial conditions. Our results are in sharp contrast with the well-studied case of exponentially bounded initial conditions. |
| |
Keywords: | Reaction-diffusion equations Initial data Slow decay Accelerating fronts |
本文献已被 ScienceDirect 等数据库收录! |