Remarks on two connected papers about Keller-Segel systems with nonlinear production

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:501

Article

Tanaka, Yuya¹  Viglialoro, Giuseppe²  Yokota, Tomomi¹ 

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan

[2] Univ Cagliari, Dipartimento Matemat & Informat, Via Osped 72, I-09124 Cagliari, Italy

关键词: Chemotaxis;    Nonlinear diffusion;    Nonlinear production;    Global boundedness;   

DOI  :  10.1016/j.jmaa.2021.125188

来源: Elsevier

【 摘 要 】

These notes aim to provide a deeper insight on the specifics of two articles dealing with chemotaxis models with nonlinear production. More precisely, we are referring to the papers Boundedness of solutions to a quasilinear parabolic-parabolic chemotaxis model with nonlinear signal production by Tao et al. (2019) [2] and Boundedness for a fully parabolic Keller-Segel model with sublinear segregation and superlinear aggregation by Frassu and Viglialoro (2021) [1]. These works, independently published in these last years, present results leaving open room for further improvement. Indeed, in the first a gap in the proof of the main claim appears, whereas the cornerstone assumption in the second is not sharp. In these pages we give a more complete picture to the relative underlying comprehension. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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