Journal
NONLINEARITY
Volume 31, Issue 1, Pages 108-164Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/aa8ca7
Keywords
KPP nonlinearities; reaction-diffusion system; steady states; structured population; traveling waves
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This paper is concerned with non-cooperative parabolic reaction-diffusion systems which share structural similarities with the scalar Fisher-KPP equation. These similarities make it possible to prove, among other results, an extinction and persistence dichotomy and, when persistence occurs, the existence of a positive steady state, the existence of traveling waves with a half-line of possible speeds and a positive minimal speed and the equality between this minimal speed and the spreading speed for the Cauchy problem. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and superlinear competition.
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