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

Abstract

In this paper, we consider the global well-posedness of solutions to a para-bolic-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.

Keywords

Keller-Segel model / p-Laplacian / strong solution / boundedness / decay rate