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Title of Journal: Arch Rational Mech Anal

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Abbravation: Archive for Rational Mechanics and Analysis

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Springer Berlin Heidelberg

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10.1002/cncr.11799

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1432-0673

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Generalized Transition Fronts for OneDimensional

Authors: Grégoire Nadin Luca Rossi
Publish Date: 2016/11/01
Volume: 223, Issue: 3, Pages: 1239-1267
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Abstract

This paper investigates the existence of generalized transition fronts for FisherKPP equations in onedimensional almost periodic media Assuming that the linearized elliptic operator near the unstable steady state admits an almost periodic eigenfunction we show that such fronts exist if and only if their average speed is above an explicit threshold This hypothesis is satisfied in particular when the reaction term does not depend on x or in some cases is small enough Moreover except for the threshold case the fronts we construct and their speeds are almost periodic in a sense When our hypothesis is no longer satisfied such generalized transition fronts still exist for an interval of average speeds with explicit bounds Our proof relies on the construction of sub and super solutions based on an accurate analysis of the properties of the generalized principal eigenvalues

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