  The stability of the 1+1 dimensional solution of Israel-Stewart theory is
investigated. Firstly, the evolution of the temperature and the ratio of the
bulk pressure over the equilibrium pressure of the background is explored. Then
the stability with linear perturbations is studied by using the Lyapunov direct
method. It shows that the shear viscosity may weaken the instability induced by
the large peak of bulk viscosity around the phase transition temperature $T_c$.
