In this paper we establish a Morse decomposition of the stationary solutions of the one-dimensional viscous Cahnâ€“Hilliard equation by explicit energy calculations. Strong non-degeneracy of theâ€¦ (More)

A hyperbolic flow by mean curvature equation, l t #cv"i, for the evolution of interfaces is studied. Here v, i and l t are the normal velocity, curvature and normal acceleration of the interface. Aâ€¦ (More)

The long time behavior for the degenerate Cahn-Hilliard equation [4, 5, 10], ut = âˆ‡ Â· (1âˆ’ u)âˆ‡ [Î˜ 2 {ln(1 + u)âˆ’ ln(1âˆ’ u)} âˆ’ Î±uâˆ’ 4u ] , is characterized by the growth of domains in which u(x, t) â‰ˆ uÂ±,â€¦ (More)

The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and low concentration are formed, then coarsen or grow in average size. Ofâ€¦ (More)

We consider the following hyperbolic system of PDEs which generalize the classical phase field equations with a non-conserved order parameter / and temperature u: u tt #e2/ tt #c 1 u t #e2c 1 / tâ€¦ (More)

We consider the following hyperbolic system of PDE's which generalize the classical phase eld equations with a non-conserved order parameter and temperature u: 8 < : u tt + 2 tt + 1 u t + 2 1 t = u;â€¦ (More)

Abstract. We present a phenomenological theory for phase transition dynamics with memory which yields a hyperbolic generalization of the classical phase field model when the relaxation kernels areâ€¦ (More)

The Sivashinsky equation is an asymptotically derived model equation for evolution of the solid-liquid interface which occurs during directional solidification of dilute binary alloys. During theâ€¦ (More)