Study on a growth-expansion model with chemotaxis in nutrient-replete environments.

We consider the no-flux initial-boundary value problem for the growth-expansion model with chemotaxis in nutrient-replete environments in smoothly bounded domains Ω ⊂ ℝ n . It is shown that if n = 1 or if n = 2 under some structural assumptions on parameter functions therein, for any suitably regular initial data the problem admits a unique global bounded classical solution. For any dimensions n ≥ 3 , we also prove that the problem has a unique global classical solution which is bounded under a small assumption on the initial data. Moreover, we obtain that these solutions stabilize to a uniquely determined spatially uniform equilibrium. We also provide exponential rates of convergence of solutions in a special case. [ABSTRACT FROM AUTHOR]