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• W2964302011 abstract "The current series of three papers is concerned with the asymptotic dynamics in the following parabolic–elliptic chemotaxis system with space- and time-dependent logistic source: [Formula: see text] where [Formula: see text] is a positive integer, [Formula: see text] and [Formula: see text] are positive constants, and the functions [Formula: see text] and [Formula: see text] are positive and bounded. In the first of the series, we investigate the persistence and asymptotic spreading in [Formula: see text]. To this end, under some explicit condition on the parameters, we first show that [Formula: see text] has a unique nonnegative time global classical solution [Formula: see text] with [Formula: see text] for every [Formula: see text] and every nonnegative bounded and uniformly continuous initial function [Formula: see text]. Next we show the pointwise persistence phenomena of the solutions in the sense that, for any solution [Formula: see text] of [Formula: see text] with strictly positive initial function [Formula: see text], there are [Formula: see text] such that [Formula: see text] and show the uniform persistence phenomena of solutions in the sense that there are [Formula: see text] such that for any strictly positive initial function [Formula: see text], there is [Formula: see text] such that [Formula: see text] We then discuss the spreading properties of solutions to [Formula: see text] with compactly supported initial function and prove that there are positive constants [Formula: see text] such that for every [Formula: see text] and every nonnegative initial function [Formula: see text] with nonempty compact support, we have that [Formula: see text] and [Formula: see text] We also discuss the spreading properties of solutions to [Formula: see text] with front-like initial functions. In the second and third of the series, we will study the existence, uniqueness, and stability of strictly positive entire solutions of [Formula: see text] and the existence of transition fronts of [Formula: see text], respectively." @default.
• W2964302011 created "2019-07-30" @default.
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• W2964302011 date "2018-10-01" @default.
• W2964302011 modified "2023-09-26" @default.
• W2964302011 title "Parabolic–elliptic chemotaxis model with space–time-dependent logistic sources on ℝN. I. Persistence and asymptotic spreading" @default.
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• W2964302011 doi "https://doi.org/10.1142/s0218202518400146" @default.
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