Stability of Cahn-Hilliard fronts

Bricmont, Jean;Kupiainen, Antti;Taskinen, J
(1999) Communications on Pure and Applied Mathematics — Vol. 52, n° 7, p. 839-871 (1999)

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  • Bricmont, JeanUCLouvain
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  • Kupiainen, AnttiUCLouvain
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  • Taskinen, J
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Abstract
We prove stability of the kink solution of the Cahn-Hilliard equation partial derivative(t)u = partial derivative(x)(2)(-partial derivative(x)(2)u - u/2 + u(3)/2), x is an element of R. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t --> infinity. We prove stability of the kink solution of the Cahn-Hilliard equation partial derivative(t)u = partial derivative(x)(2)(-partial derivative(x)(2)u - u/2 + u(3)/2), x is an element of R. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t --> infinity. (C) 1999 John Wiley & Sons, Inc.
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Bricmont, J., Kupiainen, A., & Taskinen, J. (1999). Stability of Cahn-Hilliard fronts. Communications on Pure and Applied Mathematics, 52(7), 839-871. https://doi.org/10.1002/(SICI)1097-0312(199907)52:7<839::AID-CPA4>3.0.CO;2-I (Original work published 1999)