Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems

Abstract

Our aim is to prove the existence and uniqueness of solutions for one-dimensional Cahn-Hilliard and Allen-Cahn type equations based on a modification of the Ginzburg-Landau free energy proposed in [8]. In particular, the free energy contains an additional term called Willmore regularization and takes into account strong anisotropy effects.

Keywords

• Cahn-Hilliard equation
• Allen-Cahn equation
• well-posedness
• Willmore regularization