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

The chemotaxis-consumption system with generalized logistic source {ut=Delta u-del . (uS(x,u,v). del v)+lambda u-mu u(alpha), x is an element of Omega, t>0, v(t)=Delta v-uv, x is an element of Omega, t>0, is considered under homogeneous Neumann boundary conditions in a bounded smooth domain Omega subset of R-n(n >= 1) with suitably regular positive initial data. Here lambda, mu > 0, alpha > 1 and S is an element of C-2(Omega x [0,infinity)(2); R-nxn) 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 ((lambda/mu)(1/alpha-1),0 in the large time limit.

Automated summary

The study investigates a chemotaxis-consumption system with generalized logistic source, constructing globally defined solutions and proving their convergence to spatially homogeneous equilibrium in the large time limit.