  Isothermal compressible two-phase flows with and without phase transition are
modeled, employing Darcy's and/or Forchheimer's law for the velocity field. It
is shown that the resulting systems are thermodynamically consistent in the
sense that the available energy is a strict Lyapunov functional. In both cases,
the equilibria are identified and their thermodynamical stability is
investigated by means of a variational approach. It is shown that the problems
are well-posed in an $L_p$-setting and generate local semiflows in the proper
state manifolds. It is further shown that a non-degenerate equilibrium is
dynamically stable in the natural state manifold if and only if it is
thermodynamically stable. Finally, it is shown that a solution which does not
develop singularities exists globally and converges to an equilibrium in the
state manifold.
