The existence, uniqueness, stability and regularity properties of traveling wave solutions of a bistable nonlinear integrodifferential equation=20 are established, as well as their global asymptoticâ€¦ (More)

The gradient flow approach to the Cahn-Hilliard and phase field models is developed, and some basic mathematical properties of the models, especially phase separation phenomena, are reviewed.

The pape r is concerned with the a sympto t i c behav io r as t ~ ~ of so lu t ions u(x, t) of the equa t ion u t uxxf (u ) = O, x ~ ( ~ , ~) , in the case f ( 0 ) = f ( 1 ) = 0 , with f(u) non-pos iâ€¦ (More)

The object of this note is to demonstrate the applicability of the methods of nonlinear functional analysis in the investigation of a complex physical problem. In 1910 T. von Karman [9] introduced aâ€¦ (More)

A free boundary problem due to Nishiura and Ohnishi is solved in one space dimension. That problem was derived, during their study of phase separation phenomena in diblock copolymers, as anâ€¦ (More)

We study certain approximate solutions of a system of equations formulated in an earlier paper (Physica D 43 44â€“62 (1990)) which in dimensionless form are ut + Î³w(Ï†)t = âˆ‡u, Î± Ï†t = âˆ‡Ï†+ F (Ï†, u), whereâ€¦ (More)

A phase field model with order parameter, concentration, and temperature as field variables is used to study the properties of solidification fronts in a binary alloy. As in previous papers, theâ€¦ (More)

A general class of nonlinear evolution equations is described, which support stable spatially oscillatory steady solutions. These equations are composed of an indefinite self-adjoint linear operatorâ€¦ (More)

Recent efforts by the present authors have focused on the fundamental multiscaling behaviors of the time averaged dynamical equations of wall-turbulence. These efforts have generated a number of newâ€¦ (More)