Global Existence and Boundedness in a Supercritical Quasilinear Degenerate Keller–Segel System Under Relaxed Smallness Conditions for Initial Data

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 + 2 n , then the system has a global weak solution under smallness conditions for initial data, where m de...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2022-08, Vol.180 (1), Article 3
Main Authors: Ogawa, Tsukasa, Yokota, Tomomi
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
Probability Theory and Stochastic Processes
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Summary: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 + 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 + 2 n < q < m + 4 n + 2 and to relax the conditions assumed in Ishida and Yokota (J. Differ. Equ. 252:2469–2491, 2012 ).
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-022-00504-y