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<p>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 <i>d</i> = 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年5月20日

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  • Jihui Wu,
  • Leiyu Yang,
  • Lei Lu

摘要

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.