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Title: | Global stabilization of the full attraction-repulsion Keller-Segel system | Authors: | Jin, HY Wang, ZA |
Issue Date: | Jun-2020 | Source: | Discrete and continuous dynamical systems. Series A, June 2020, v. 40, no. 6, p. 3509-3527 | Abstract: | We are concerned with the following full Attraction-Repulsion Keller-Segel (ARKS) system ut = ∆u − ∇ · (χu∇v) + ∇ · (ξu∇w), x ∈ Ω, t > 0, vt = D1∆v + αu − βv, x ∈ Ω, t > 0, wt = D2∆w + γu − δw, x ∈ Ω, t > 0, u(x, 0) = u0(x), v(x, 0) = v0(x), w(x, 0) = w0(x) x ∈ Ω, (∗) in a bounded domain Ω ⊂ R2 with smooth boundary subject to homogeneous Neumann boundary conditions. By constructing an appropriate Lyapunov functions, we establish the boundedness and asymptotical behavior of solutions to the system with large initial data (u0, v0, w0) ∈ [W1,∞(Ω)]3 . Precisely, we show that if the parameters satisfy ξγ χα ≥ max n D1 D2 , D2 D1 , β δ , δ β o for all positive parameters D1, D2, χ, ξ, α, β, γ and δ, the system has a unique global classical solution (u, v, w), which converges to the constant steady state (¯u0, α β u¯0, γ δ u¯0) as t → +∞, where ¯u0 = 1 |Ω| R Ω u0dx. Furthermore, the decay rate is exponential if ξγ χα > max n β δ , δ β o . This paper provides the first results on the full ARKS system with unequal chemical diffusion rates (i.e. D1 =/= D2) in multi-dimensions. [Abstract not complete, refer to publisher pdf] |
Keywords: | Chemotaxis Attraction-repulsion Global stability Exponential decay rate |
Publisher: | American Institute of Mathematical Sciences | Journal: | Discrete and continuous dynamical systems. Series A | ISSN: | 1078-0947 | EISSN: | 1553-5231 | DOI: | 10.3934/dcds.2020027 | Rights: | This article is made available under the CC-BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/) The following publication Jin, H. Y., & Wang, Z. A. (2020). Global stabilization of the full attraction-repulsion Keller-Segel system. Discrete & Continuous Dynamical Systems, 40(6), 3509 is available at https://doi.org/10.3934/dcds.2020027. |
Appears in Collections: | Journal/Magazine Article |
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