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Interfaces for 1-D degenerate Keller–Segel systems

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Abstract

Let us consider the Keller–Segel system of degenerate type (KS) m with m >1 below. We prove the property of finite speed of propagation for weak solutions u with a certain regularity. Moreover, we investigate the interface curve \({\xi(t)}\) which separates the regions \({\{(x, t) \in {\mathbb R} \times (0, T); u(x, t) > 0\}}\) and \({\{(x, t) \in {\mathbb R} \times (0, T); u(x, t) = 0\}}\) . Concretely, we characterize the interface curve as the solution of a certain ordinary differential equation associated with (KS) m .

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  1. Department of Mathematics, Tsuda University, 2-1-1, Tsuda-chou, Kodaira-shi, Tokyo, 187-8577, Japan

    Yoshie Sugiyama

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  1. Yoshie Sugiyama
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Correspondence to Yoshie Sugiyama.

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Sugiyama, Y. Interfaces for 1-D degenerate Keller–Segel systems. J. Evol. Equ. 9, 123–142 (2009). https://doi.org/10.1007/s00028-009-0001-2

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