Large time behavior of solution to an attraction-repulsion chemotaxis system with logistic source in three dimensions
The authors consider the non-homogeneous quasilinear diffusion-transport problem in a convex bounded smooth domain in \(\mathbb R^3\). Boundary conditions are Neumann homogeneous. The source function \(f(u)=u(1-\mu u^\gamma)\), \(\gamma\geq1\), \(\mu>0\), depends on one unknown function. Global existence and asymptotic stability of a unique bounded solution are proven under assumption that initial distributions are from \(W^{1,\infty}\) and some inequalities for parameters hold. Also, convergence of the solution to the steady state in \(L^\infty\) is shown.
scientific article; zbMATH DE number 6668543
scientific article