@Article{CSIAM-AM-5-671,
author = {Lu , Yi and Jin , Chunhua},
title = {Global Solvability and Decay Properties for a $p$-Laplacian Diffusive Keller-Segel Model},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2024},
volume = {5},
number = {4},
pages = {671--711},
abstract = {<p style="text-align: justify;">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 $p&gt; p^∗,$ the solution exists globally for arbitrary large initial value. When $1&lt;p≤p^∗,$ 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.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2022-0038},
url = {http://global-sci.org/intro/article_detail/csiam-am/23584.html}
}