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- W3189642720 abstract "This article deals with a fully parabolic chemotaxis system describing the behavior of a biological species with density “u” which follows a chemical gradient with density “v”. The problem presents a nonlocal growth term defined by f(u)=ua0−a1uα+a2∫Ωuαdxand the system is given by the following two second order coupled parabolic equations ut−Δu=−div(χum∇v)+f(u),vt−Δv+v=uγ,in a bounded domain Ω with homogeneous Neumann boundary conditions and appropriate initial data. The parameters α, m, ai (i=1,2) and γ satisfy α≥1,m>1,γ≥1,α+1>m+γ,a1>0,a1−a2|Ω|>0.Under suitable assumptions on the initial data and the coefficients of the system, the global-in-time existence of classical solutions and the convergence to the steady state u∗=a01α(a1−a2|Ω|)1α,v∗=(u∗)γ,when a0>0, are proved in any space dimension." @default.
- W3189642720 created "2021-08-16" @default.
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- W3189642720 date "2021-12-01" @default.
- W3189642720 modified "2023-09-27" @default.
- W3189642720 title "On a fully parabolic chemotaxis system with nonlocal growth term" @default.
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- W3189642720 doi "https://doi.org/10.1016/j.na.2021.112518" @default.
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