Multidimensional transition fronts for Fisher–KPP reactions

Abstract

We study entire solutions to homogeneous reaction-diffusion equations in several dimensions with Fisher-KPP reactions. Any entire solution 0 < u < 1 is known to satisfy lim t→−∞ sup|x|≤c|t| u(t,x) = 0 for each c < 2√f′(0), and we consider here those satisfying lim t→−∞ sup|x|≤c|t| u(t,x) = 0 for some c > 2√f′(0). When f is C_2 and concave, our main result provides an almost complete characterization of transition fronts as well as transition solutions with bounded width within this class of solutions.

Additional Information

© 2019 IOP Publishing Ltd & London Mathematical Society. Received 20 March 2018; Accepted 13 November 2018; Published 8 February 2019. AZ was supported in part by NSF grants DMS-1147523, DMS-1656269, and DMS-1652284. AA and JL were supported in part by NSF grant DMS-1147523. ZH and ZT were supported in part by NSF grant DMS-1656269. AA, ZH, and ZT gratefully acknowledge the hospitality of the Department of Mathematics at the University of Wisconsin–Madison during the REU "Differential Equations and Applied Mathematics", where this research originated.

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