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

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 an 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.