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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Published in:Acta applicandae mathematicae 2022-08, Vol.180 (1), Article 3
Main Authors: Ogawa, Tsukasa, Yokota, Tomomi
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Language:English
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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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description 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 ).
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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
title Global Existence and Boundedness in a Supercritical Quasilinear Degenerate Keller–Segel System Under Relaxed Smallness Conditions for Initial Data
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