Hyperbolic non-conserved phase field equations

We consider the following hyperbolic system of PDEs which generalize the cl assical phase held equations with a non-conserved order parameter phi and t emperature u: u(tt) + epsilon(2)phi(tt) + y(1)u(t) + epsilon(2)y(1)phi(t) = alpha Delta u, epsilon(2)phi(tt) + y(2)epsilon(2)phi(t) = epsilon(2)Delta phi f(phi) + epsilon u for epsilon much less than 1. We present the model, derive a law for the evolution of the interface which generalizes the class ical flow by mean curvature equation, and analyze the evolution of some sim ply shaped interfaces. (C) 1999 Elsevier Science B.V. All rights reserved. PACS: 64.70.Dv.