Luca Rossi
Published 2015-03-31Version 1
The Freidlin-G\"artner formula expresses the asymptotic speed of spreading for spatial-periodic Fisher-KPP equations in terms of the principal eigenvalues of a family of linear operators. One cannot expect the same formula to hold true for the other classes of reaction terms: monostable, combustion and bistable. However, these eigenvalues have been later related to the minimal speeds of pulsating travelling fronts, yielding a formula for the spreading speed which is not unreasonable to expect to hold for any reaction term. We show here that it is indeed the case. The method is based on a new geometric approach which provides a rather simple PDE proof of Freidlin-G\"artner's result. It is developed for equations whose terms depend arbitrarily on time and space, highlighting a connection between the asymptotic speed of spreading and almost planar transition fronts.
Neumann $p$-Laplacian problems with a reaction term on metric spaces
On a nonlocal Cahn-Hilliard equation with a reaction term
How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?
![QR code for arXiv:1503.09010 [math.AP]](http://oss.arxitics.com/images/favicon.svg)