Fast propagation for KPP equations with slowly decaying initial conditions - Mathematics > Analysis of PDEsReport as inadecuate




Fast propagation for KPP equations with slowly decaying initial conditions - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: This paper is devoted to the analysis of the large-time behavior of solutionsof one-dimensional Fisher-KPP reaction-diffusion equations. The initialconditions are assumed to be globally front-like and to decay at infinitytowards the unstable steady state more slowly than any exponentially decayingfunction. We prove that all level sets of the solutions move infinitely fast astime goes to infinity. The locations of the level sets are expressed in termsof the decay of the initial condition. Furthermore, the spatial profiles of thesolutions become asymptotically uniformly flat at large time. This papercontains the first systematic study of the large-time behavior of solutions ofKPP equations with slowly decaying initial conditions. Our results are in sharpcontrast with the well-studied case of exponentially bounded initialconditions.



Author: Francois Hamel LATP, Lionel Roques BioSP

Source: https://arxiv.org/







Related documents