Asymptotic profile of a parabolic–hyperbolic system with boundary effect arising from tumor angiogenesis

This paper concerns a parabolic–hyperbolic system on the half space R+R+ with boundary effect. The system is derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. We show that the solution of the system subject to appropriate boundary conditions converges to a traveling wave profile as time tends to infinity if the initial data is a small perturbation around the wave which is shifted far away from the boundary but its amplitude can be arbitrarily large.