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AIMS Mathematics, 2016, 1(3): 156-164. doi: 10.3934/Math.2016.3.156 Research article

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Remarks on smallness of chemotactic effect for asymptotic stability in a two-species chemotaxis system

Masaaki Mizukami

Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

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This paper deals with the two-species chemotaxis system

where Ω is a bounded domain in R^N with smooth boundary ∂Ω, N∈N; h,X_i are functions satisfying some conditions. Global existence and asymptotic stability of solutions to the above system were established under some conditions [11]. The main purpose of the present paper is to improve smallness conditions for chemotactic effect deriving asymptotic stability and to give the convergence rate in stabilization which cannot be attained in the previous work.

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Keywords: Chemotaxis; Sensitivity function; Logistic term; Asymptotic behavior; Stability

Citation: Masaaki Mizukami. Remarks on smallness of chemotactic effect for asymptotic stability in a two-species chemotaxis system. AIMS Mathematics, 2016, 1(3): 156-164. doi: 10.3934/Math.2016.3.156

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Copyright Info: © 2016, Masaaki Mizukami, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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