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.