Publications [#244196] of Thomas P. Witelski

Papers Published

1. Witelski, TP, The structure of internal layers for unstable nonlinear diffusion equations, Studies in Applied Mathematics, vol. 97 no. 3 (January, 1996), pp. 277-300, WILEY [gz], [doi]
   (last updated on 2024/04/17)

   Abstract:
   We study the structure of diffusive layers in solutions of unstable nonlinear diffusion equations. These equations are regularizations of the forward-backward heat equation and have diffusion coefficients that become negative. Such models include the Cahn-Hilliard equation and the pseudoparabolic viscous diffusion equation. Using singular perturbation methods we show that the balance between diffusion and higher-order regularization terms uniquely determines the interface structure in these equations. It is shown that the well-known "equal area" rule for the Cahn-Hilliard equation is a special case of a more general rule for shock construction in the viscous Cahn-Hilliard equation.