Math @ Duke

Publications [#244196] of Thomas P. Witelski
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 Witelski, TP, The structure of internal layers for unstable nonlinear diffusion equations,
Studies in Applied Mathematics, vol. 97 no. 3
(1996),
pp. 277300 [gz]
(last updated on 2018/02/24)
Abstract: We study the structure of diffusive layers in solutions of unstable nonlinear diffusion equations. These equations are regularizations of the forwardbackward heat equation and have diffusion coefficients that become negative. Such models include the CahnHilliard equation and the pseudoparabolic viscous diffusion equation. Using singular perturbation methods we show that the balance between diffusion and higherorder regularization terms uniquely determines the interface structure in these equations. It is shown that the wellknown "equal area" rule for the CahnHilliard equation is a special case of a more general rule for shock construction in the viscous CahnHilliard equation.


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