The Relaxation Limit of a Quasi-Linear Hyperbolic-Parabolic Chemotaxis System Modeling Vasculogenesis

Abstract

This paper is concerned with the relaxation limit of a three-dimensional quasi-linear hyperbolic-parabolic chemotaxis system modeling vasculogenesis when the initial data are prescribed around a constant ground state. When the relaxation time tends to zero (i.e. the damping is strong), we show that the strong-weak limit of the cell density and chemoattractant concentration satisfies a parabolic-elliptic Keller-Segel type chemotaxis system in the sense of distribution.