Global bounded weak solutions to a degenerate quasilinear chemotaxis system with rotation |
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| Authors: | Yilong Wang |
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| Affiliation: | 1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;2. School of Sciences, Southwest Petroleum University, Chengdu 610500, China |
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| Abstract: | This paper deals with the quasilinear Keller–Segel system with rotation ![urn:x-wiley:mma:media:mma3561:mma3561-math-0006]( "urn:x-wiley:mma:media:mma3561:mma3561-math-0006") where  is a bounded domain with smooth boundary, D(u) is supposed to be sufficiently smooth and satisfies D(u)≥D0um ? 1(m≥1) and D(u)≤D1(u + 1)K ? mum ? 1(K≥1) for all u≥0 with some positive constants D0 and D1, and f(u) is assumed to be smooth enough and non‐negative for all u≥0 and f(0) = 0, while S(u,v,x) = (sij)n × n is a matrix with  and  with l≥2, where  is nondecreasing on 0,∞). It is proved that when  , the system possesses at least one global and bounded weak solution for any sufficiently smooth non‐negative initial data. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | chemotaxis boundedness rotation global existence |
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