From the viscous Cahn–Hilliard equation to a regularized forward-backward parabolic equation

Article type: Research Article

Authors: Colli, Pierluigi^{a; *} | Scarpa, Luca^b

Affiliations: [a] Dipartimento di Matematica “F. Casorati”, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy. E-mail: pierluigi.colli@unipv.it | [b] Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom. E-mail: luca.scarpa.15@ucl.ac.uk

Correspondence: [*] Corresponding author. E-mail: pierluigi.colli@unipv.it.

Abstract: A rigorous proof is given for the convergence of the solutions of a viscous Cahn–Hilliard system to the solution of the regularized version of the forward-backward parabolic equation, as the coefficient of the diffusive term goes to 0. Non-homogenous Neumann boundary conditions are handled for the chemical potential and the subdifferential of a possible non-smooth double-well functional is considered in the equation. An error estimate for the difference of solutions is also proved in a suitable norm and with a specified rate of convergence.

Keywords: Cahn–Hilliard system, forward-backward parabolic equation, viscosity, initial-boundary value problem, asymptotic analysis, well-posedness

DOI: 10.3233/ASY-161380

Journal: Asymptotic Analysis, vol. 99, no. 3-4, pp. 183-205, 2016