  In this paper we investigate quasilinear parabolic systems of conserved
Penrose-Fife type. We show maximal $L_p$ - regularity for this problem with
inhomogeneous boundary data. Furthermore we prove global existence of a
solution, provided that the absolute temperature is bounded from below and
above. Moreover, we apply the Lojasiewicz-Simon inequality to establish the
convergence of solutions to a steady state as time tends to infinity.
