  A new phase field model is introduced, which can be viewed as nontrivial
generalisation of what is known as the Caginalp model. It involves in
particular nonlinear diffusion terms. By formal asymptotic analysis, it is
shown that in the sharp interface limit it still yields a Stefan-like model
with: 1) a (generalized) Gibbs-Thomson relation telling how much the interface
temperature differs from the equilibrium temperature when the interface is
moving or/and is curved with surface tension; 2) a jump condition for the heat
flux, which turns out to depend on the latent heat and on the velocity of the
interface with a new, nonlinear term compared to standard models. From the PDE
analysis point of view, the initial-boundary value problem is proved to be
locally well-posed in time (for smooth data).
