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Global Solvability and Decay Properties for a $p$-Laplacian Diffusive Keller-Segel Model

Global Solvability and Decay Properties for a $p$-Laplacian Diffusive Keller-Segel Model

Year:    2024

Author:    Yi Lu, Chunhua Jin

CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 4 : pp. 671–711

Abstract

In this paper, we consider the global well-posedness of solutions to a parabolic-parabolic Keller-Segel model with $p$-Laplace diffusion. We first establish a critical exponent $p^∗=3N/(N+1)$ and prove that when $p> p^∗,$ the solution exists globally for arbitrary large initial value. When $1<p≤p^∗,$ there exists a uniformly bounded global strong solution for small initial value, and the solution decays to zero as $t→ ∞.$ This paper improves and expands the results of [Cong and Liu, Kinet. Relat. Models, 9(4), 2016], in which the parabolic-elliptic case is studied.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.SO-2022-0038

CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 4 : pp. 671–711

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    41

Keywords:    Keller-Segel model $p$-Laplacian strong solution boundedness decay rate.

Author Details

Yi Lu

Chunhua Jin