Geodesic
Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems
Electronic journal of differential equations, Tome 2015 (2015)
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.
Classification : 35B45, 35K55
Keywords: Cahn-Hilliard equation, Allen-Cahn equation, well-posedness, willmore regularization 
@article{EJDE_2015__2015__a25,
     author = {Makki,  Ahmad and Miranville,  Alain},
     title = {Well-posedness for one-dimensional anisotropic {Cahn-Hilliard} and {Allen-Cahn} systems},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1334.35106},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a25/}
}
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%A Miranville,  Alain
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Makki,  Ahmad; Miranville,  Alain. Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a25/