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Mathematical Modelling
Recent results on the Cahn–Hilliard equation with dynamic boundary conditions
P. Colliab, G. Gilardiab, J. Sprekelscd a Research Associate at the IMATI – C.N.R. PAVIA, Pavia, Italy
b Dipartimento di Matematica "Felice Casorati", Università di Pavia
c Weierstrass Institute for Applied Analysis and Stochastics
d Humboldt-Universität zu Berlin, Berlin, Germany
Abstract:
The pure or viscous Cahn–Hilliard equation with possibly singular potentials and dynamic boundary conditions is considered and the well-posedness of the related initial value problem is discussed. Then, a boundary control problem for the viscous Cahn–Hilliard system is studied and first order necessary conditions for optimality are shown. Moreover, the same boundary control problem is addressed for the pure Cahn–Hilliard system, by investigating it and passing to the limit in the analogous results for the viscous Cahn–Hilliard system as the viscosity coefficient tends to zero.
Keywords:
Cahn–Hilliard equation; dynamic boundary conditions; phase separation; well-posedness; boundary control problem; optimality conditions.
Received: 30.11.2016
Citation:
P. Colli, G. Gilardi, J. Sprekels, “Recent results on the Cahn–Hilliard equation with dynamic boundary conditions”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:1 (2017), 5–21
Linking options:
https://www.mathnet.ru/eng/vyuru355 https://www.mathnet.ru/eng/vyuru/v10/i1/p5
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Abstract page: | 194 | Full-text PDF : | 65 | References: | 35 |
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