Stabilization in a high‐dimensional chemotaxis system involving arbitrary superlinear degradation

Abstract

The chemotaxis‐consumption system with generalized logistic source is considered under homogeneous Neumann boundary conditions in a bounded smooth domain with suitably regular positive initial data. Here λ, μ > 0, α > 1 and is a given matrix‐valued function. We construct globally defined solutions in an appropriately generalized sense and prove that these solutions converge to the spatially homogeneous equilibrium in the large time limit.