Global Solvability and Decay Properties for a $p$-Laplacian Diffusive Keller-Segel Model (CSIAM Transactions on Applied Mathematics, 2024)
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
Keywords: Keller-Segel model; $p$-Laplacian; strong solution; boundedness; decay rate.