The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn--Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a suitable setting for the conservation of a total mass in the bulk plus the boundary. A very general class of double-well like potentials is allowed. Moreover, some further regularity is obtained to guarantee the strong solution.
Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials
COLLI, PIERLUIGI;
2015-01-01
Abstract
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn--Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a suitable setting for the conservation of a total mass in the bulk plus the boundary. A very general class of double-well like potentials is allowed. Moreover, some further regularity is obtained to guarantee the strong solution.File in questo prodotto:
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