Large time behavior of a hyperbolic-parabolic model of vasculogenesis

In this paper, we mainly consider the Cauchy problem of a hyperbolic-parabolic model vasculogenesis in dimension three. We first obtain optimal $ L^2 $-decay rate solution and its highest order derivatives when initial perturbation is small H^3(\mathbb{R}^3) bounded L^1(\mathbb{R}^3) $. Here, optimality means there no decay loss for highest-order spatial derivatives. This refines that [21], where only was given H^4\cap Next, derive space-time descriptions based on analysis Green's function.