TY - JOUR
T1 - Global Solvability and Decay Properties for a $p$-Laplacian Diffusive Keller-Segel Model
AU - Lu , Yi
AU - Jin , Chunhua
JO - CSIAM Transactions on Applied Mathematics
VL - 4
SP - 671
EP - 711
PY - 2024
DA - 2024/11
SN - 5
DO - http://doi.org/10.4208/csiam-am.SO-2022-0038
UR - https://global-sci.org/intro/article_detail/csiam-am/23584.html
KW - Keller-Segel model, $p$-Laplacian, strong solution, boundedness, decay rate.
AB - <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>