Cahn–Hilliard Approach to Some Degenerate Parabolic Equations with Dynamic Boundary Conditions

Abstract : In this paper the well-posedness of some degenerate parabolic equations with a dynamic boundary condition is considered. To characterize the target degenerate parabolic equation from the Cahn–Hilliard system, the nonlinear term coming from the convex part of the double-well potential is chosen using a suitable maximal monotone graph. The main topic of this paper is the existence problem under an assumption for this maximal monotone graph for treating a wider class. The existence of a weak solution is proved.
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Takeshi Fukao. Cahn–Hilliard Approach to Some Degenerate Parabolic Equations with Dynamic Boundary Conditions. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.282-291, ⟨10.1007/978-3-319-55795-3_26⟩. ⟨hal-01626916⟩

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