Analysis of long‐time solution of chemotactic model with indirect signal consumption in three‐dimensional case

Abstract

In this paper, we consider the following chemotaxis model with indirect signal consumption: under the homogeneous Neumann boundary conditions for and in a bounded convex domain with smooth boundary, where is a given parameter. It is shown that for each , the global weak solutions exist whenever the initial data are sufficiently regular satisfying and . Moreover, it is proved that the global solution converges to in as . In particular, we extend the recent result of Liu–Li–Huang [Y Liu, Z Li and J Huang, Global boundedness and large time behavior of a chemotaxis system with indirect signal absorption, J. Differential Equations 269 (2020) 6365‐6399] to the nonlinear diffusion case.