Abstract: By using the time-weighted energy method, we discussed  the global existence and the asymptotic behavior of solutions near the constant equilibrium state of  the Cauchy problem on a hyperbolic-parabolic model for vasculogenesis. The results show  that the density, the velocity and the chemical attractant concentration converge to the constant equilibrium state with the decay rate (1+t)^-3/4 in the sense of L² norm when  the pressure P and the far field state ρ of initial density satisfy that bP′(ρ)-aμρ>0.

Key words: vasculogenesis model, large-time behavior, energy estimate, decay estimate