EVENTUAL SMOOTHNESS AND STABILIZATION OF GLOBAL WEAK SOLUTIONS TO A CHEMOTAXIS SYSTEM WITH SUBLINEAR CONSUMPTION OF CHEMOATTRACTANT

This paper investigates a chemotaxis system with sublinear consumption of chemoattractant {u(t) = Delta u del center dot (u del v), (*) v(t) = Delta v - uv(m) under homogeneous Neumann boundary conditions in bounded convex domain Omega subset of R-3 with smooth boundary. We prove that if m is an element of (0, 1], for arbitrarily large initial data, then the model (*) admits at least one global weak solution for which there exists T > 0 such that (u, v) is bounded and smooth in Omega x (T, infinity). Moreover, it is asserted that such solutions are seen to stabilize toward spatially constant equilibrium in the large time limit.