Weak Solutions to the Anisotropic Degenerate Cahn–Hilliard Equation with Logarithmic Potential

Abstract

This paper is concerned with a diffusion interface model for phase separation of the anisotropic Cahn–Hilliard equation with a concentration-dependent degenerate mobility in dimensions d = 2, 3. We present the global existence of weak solutions to the non-degenerate anisotropic Cahn–Hilliard equation with a smooth double-well potential. Furthermore, we obtain the global existence and regularity of weak solutions to the anisotropic degenerate Cahn–Hilliard equation with a logarithmic potential.

Keywords

Anisotropic / Cahn–Hilliard / non-degenerate / degenerate / 35B40 / 35K55

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