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- W3044698566 abstract "In this paper we study the initial boundary value problem for the system $u_t-Delta u^m=-mbox{div}(u^{q}nabla v), v_t-Delta v+v=u$. This problem is the so-called Keller-Segel model with nonlinear diffusion. Our investigation reveals that nonlinear diffusion can prevent overcrowding. To be precise, we show that solutions are bounded as long as $m>q>0$, thereby substantially generalizing the known results in this area. Furthermore, our result seems to imply that the Keller-Segel model can have bounded solutions and blow-up ones simultaneously." @default.
- W3044698566 created "2020-07-29" @default.
- W3044698566 creator A5044607151 @default.
- W3044698566 date "2020-07-23" @default.
- W3044698566 modified "2023-09-24" @default.
- W3044698566 title "Nonlinear diffusion in the Keller-Segel model of parabolic-parabolic type" @default.
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- W3044698566 doi "https://doi.org/10.48550/arxiv.2007.11883" @default.
- W3044698566 hasPublicationYear "2020" @default.
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