Abstract
This paper is concerned with a quasilinear degenerate Keller–Segel system of parabolic–parabolic type. It was proved in Ishida and Yokota (J. Differ. Equ. 252:2469–2491, 2012) that if \(q>m+\frac{2}{n}\), then the system has a global weak solution under smallness conditions for initial data, where \(m\) describes the intensity of diffusion, \(q\) shows the nonlinearity, and \(n\) denotes the dimension. The smallness conditions were relaxed in Wang et al. (Z. Angew. Math. Phys. 70:18 pp., 2019) when \(q=2\). The purpose of this paper is to obtain global existence and boundedness under more general conditions for initial data in the case \(m+\frac{2}{n}< q< m+\frac{4}{n+2}\) and to relax the conditions assumed in Ishida and Yokota (J. Differ. Equ. 252:2469–2491, 2012).
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The authors would like to thank the anonymous referees for their fruitful comments and helpful suggestions on improving this paper.
Funding
T. Yokota partially supported by Grant-in-Aid for Scientific Research (C), No. 25400119.
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Ogawa, T., Yokota, T. Global Existence and Boundedness in a Supercritical Quasilinear Degenerate Keller–Segel System Under Relaxed Smallness Conditions for Initial Data. Acta Appl Math 180, 3 (2022). https://doi.org/10.1007/s10440-022-00504-y
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DOI: https://doi.org/10.1007/s10440-022-00504-y