Weak Solutions for the Cahn–Hilliard Equation with Degenerate Mobility
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In this paper, we study the well-posedness of Cahn–Hilliard equations with degenerate phase-dependent diffusion mobility. We consider a popular form of the equations which has been used in phase field simulations of phase separation and microstructure evolution in binary systems. We define a notion of weak solutions for the nonlinear equation. The existence of such solutions is obtained by considering the limits of Cahn–Hilliard equations with non-degenerate mobilities.
KeywordsWeak Solution Energy Inequality Degenerate Parabolic Equation Diffusion Mobility Hilliard Equation
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- 12.Royden, H.L.: Real Analysis, 3rd edn. Macmillan Publishing Company, New York, 1988Google Scholar