We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given by this cone, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity.
The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations / Berestycki, H.; Roquejoffre, J. -M.; Rossi, L.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 343:1(2016), pp. 207-232. [10.1007/s00220-015-2517-3]
The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations
Rossi L.
2016
Abstract
We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given by this cone, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity.File | Dimensione | Formato | |
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