Asymptotic Behavior of a Tumor Angiogenesis Model with Haptotaxis

This paper considers the existence and asymptotic behavior of solutions to the angiogenesis system p(t) = Delta p - rho del . (p del w) + lambda p(1 - p), w(t) = -gamma pw(beta) in a bounded smooth domain Omega subset of R-N (N = 1, 2), where rho, lambda, gamma > 0 and beta >= 1. More precisely, it is shown that the corresponding solution (p, w) converges to (1, 0) with an explicit exponential rate if beta = 1, and polynomial rate if beta > 1 as t -> infinity, respectively, in L-infinity-norm.