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• W4361763953 abstract "<abstract><p>This paper is concerned with a chemotaxis system in a two-dimensional setting as follows:</p> <p><disp-formula> <label>$star$</label> <tex-math id=E1> begin{document}$ begin{equation*} left{ begin{split} &amp;u_t = Delta u-chinablacdotleft(unablaln vright)-kappa uv+ru-mu u^2+ h_1, &amp;v_t = Delta v- v+ uv+h_2, end{split} right. end{equation*} $end{document} </tex-math></disp-formula></p> <p>with the parameters $ chi, kappa, mu &gt; 0 $ and $ rin mathbb R $, and with the given functions $ h_1, h_2geq0 $. This model was originally introduced by Short <italic>et al</italic> for urban crime with the particular values $ chi = 2, r = 0 $ and $ mu = 0 $, and the logistic source term $ ru-mu u^2 $ was incorporated into ($ star $) by Heihoff to describe the fierce competition among criminals. Heihoff also proved that the initial-boundary value problem of ($ star $) possesses a global generalized solution in the two-dimensional setting. The main purpose of this paper is to show that such a generalized solution becomes bounded and smooth at least eventually. In addition, the long-time asymptotic behavior of such a solution is discussed.</p></abstract>" @default.
• W4361763953 created "2023-04-04" @default.
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• W4361763953 date "2023-01-01" @default.
• W4361763953 modified "2023-10-06" @default.
• W4361763953 title "Eventual smoothness of generalized solutions to a singular chemotaxis system for urban crime in space dimension 2" @default.
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• W4361763953 doi "https://doi.org/10.3934/era.2023163" @default.
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