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• W3124348982 abstract "We consider a population structured by a space variable and a phenotypical trait, submitted to dispersion, mutations, growth and nonlocal competition. This population is facing an environmental gradient: to survive at location [Formula: see text], an individual must have a trait close to some optimal trait [Formula: see text]. Our main focus is to understand the effect of a nonlinear environmental gradient. We thus consider a nonlocal parabolic equation for the distribution of the population, with [Formula: see text], [Formula: see text]. We construct steady states solutions and, when [Formula: see text] is periodic, pulsating fronts. This requires the combination of rigorous perturbation techniques based on a careful application of the implicit function theorem in rather intricate function spaces. To deal with the phenotypic trait variable [Formula: see text] we take advantage of a Hilbert basis of [Formula: see text] made of eigenfunctions of an underlying Schrödinger operator, whereas to deal with the space variable [Formula: see text] we use the Fourier series expansions. Our mathematical analysis reveals, in particular, how both the steady states solutions and the fronts (speed and profile) are distorted by the nonlinear environmental gradient, which are important biological insights." @default.
• W3124348982 created "2021-02-01" @default.
• W3124348982 creator A5012220090 @default.
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• W3124348982 date "2021-12-28" @default.
• W3124348982 modified "2023-10-17" @default.
• W3124348982 title "Populations facing a nonlinear environmental gradient: Steady states and pulsating fronts" @default.
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• W3124348982 doi "https://doi.org/10.1142/s0218202522500063" @default.
• W3124348982 hasPublicationYear "2021" @default.
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