Existence of viscous shock wave of a generalized hyperbolic-parabolic system arising from chemotaxis

In this paper, we establish the existence of viscous shock waves solutions of a quasi-linear hyperbolic-parabolic system arising from chemotaxis by using of Lyapunov stability techniques. Different from T.L. and Z.A. Wang [12], we consider that the chemosensitivity constant and the kinetic constant have the same sign. Furthermore, we show that the left-hand and right-hand states of a Lax shock correspond to saddle nodes.