Recent results on the Cahn - Hilliard equation with dynamic boundary conditions

Recent results on the Cahn - Hilliard equation with dynamic boundary conditions

Автор: Colli P., Gilardi G., Sprekels J.

Журнал: Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp

Рубрика: Математическое моделирование

Статья в выпуске: 1 т.10, 2017 года.

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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.

Cahn hilliard equation, dynamic boundary conditions, phase separation, well-posedness, boundary control problem, optimality conditions

Короткий адрес: https://sciup.org/147159415

IDR: 147159415   |   DOI: 10.14529/mmp170101

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