Convergence to nonlinear diffusion waves for solutions of hyperbolic-parabolic chemotaxis system

In this paper, we investigate the Cauchy problem for a quasi-linear hyperbolic-parabolic chemotaxis system modelling vasculogenesis. As Liu, Peng and Wang pointed out in [20], the smooth solutions of Cauchy problem for this system globally exist and converge to the shifted nonlinear diffusion waves. It is worth noting that due to the difficulty in constructing a group of correction functions to eliminate the gaps between the original solutions and the diffusion waves at infinity, they got their results under the stiff conditions m+ = 0 and 0+ = ab p+. However, by a deep observation, we realize that these two conditions can be removed. In this paper, by making full use of the results obtained in [20], and with the help of a group of new correction functions, we get some more general results. (c) 2023 Elsevier Inc. All rights reserved.