Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimensions

Abstract

Then, due to the obtained qualitative bounds, upon deriving higher order gradient estimates, we show exponential convergence of bounded solutions to the spatially homogeneous equilibrium (i) for µ large relative to χ 2 + ξ 2 1 if µ > 0, (ii) for d large if a = µ = 0 and (iii) for merely d > 0 if χ = a = µ = 0. As a direct consequence of our findings, all solutions to the above system with χ = a = µ = 0 are globally bounded and they converge to constant equilibrium, and therefore, no patterns can arise.