Boundary effect on asymptotic behaviour of solution to the hyperbolic-parabolic chemotaxis system

This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular networks observed invitro experiment. Under two diffrent boundary conditions,we first establish the existence and uniqueness of the solution of the asymptotic state equation (the so-called nonlinear diffusion wave),and then prove that the solution of the original equation is nonlinearly asymptotically stable. Additionally,we obtain the convergence rates for both types of boundary conditions.