Global existence and asymptotic behavior of solutions for a hyperbolic-parabolic model of chemotaxis on network

In this paper, we discuss a hyperbolic-parabolic system on a network. The global existence of solution to this problem with suitable the transmission conditions at interior is obtained by energy estimates. Moreover, for the case of acyclic network, we prove the existence and uniqueness of stationary solution to the system and show that the stationary solution provides asymptotic profiles for a class of global solutions.