  We consider a hyperbolic-parabolic model of vasculogenesis in the
multidimensional case. For this system we show the global existence of smooth
solutions to the Cauchy problem, using suitable energy estimates. Since this
model does not enter in the classical framework of dissipative problems, we
analyze it combining the features of the hyperbolic and the parabolic parts.
Moreover we study the asymptotic behavior of those solutions showing their
decay rates by means of detailed analysis of the Green function for the
linearized problem.
