Cosmological Evolution of Interacting Phantom Energy with Dark Matter

We investigate the cosmological evolution of an interacting phantom energy model in which the phantom field has interaction with the dark matter. We discuss the existence and stability of scaling solutions for two types of specific interactions. One is motivated by the conformal transformation in string theory and the other is motivated by analogy with dissipation. In the former case, there exist no scaling solutions. In the latter case, there exist stable scaling solutions, which may give a phenomenological solution of the coincidence problem. Furthermore, the universe either accelerates forever or ends with a singularity, which is determined by not only the model parameters but also the initial velocity of the phantom field