Doubly nonlocal Cahn–Hilliard equations

Gal, Ciprian G.

doi:10.1016/j.anihpc.2017.05.001

Gal, Ciprian G.

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 357-392.

Résumé

We consider a doubly nonlocal nonlinear parabolic equation which describes phase-segregation of a two-component material in a bounded domain. This model is a more general version than the recent nonlocal Cahn–Hilliard equation proposed by Giacomin and Lebowitz [26], such that it reduces to the latter under certain conditions. We establish well-posedness results along with regularity and long-time results in the case when the interaction between the two levels of nonlocality is strong-to-weak.

MR Zbl

DOI : 10.1016/j.anihpc.2017.05.001

Classification : 35R09, 37L30, 82C24
Mots clés : Nonlocal Cahn–Hilliard, phase transition, solutions, doubly nonlocal equation, anomalous transport, fractional Laplace

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     title = {Doubly nonlocal {Cahn{\textendash}Hilliard} equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {357--392},
     publisher = {Elsevier},
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     number = {2},
     year = {2018},
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     zbl = {1387.35595},
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Gal, Ciprian G. Doubly nonlocal Cahn–Hilliard equations. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 357-392. doi : 10.1016/j.anihpc.2017.05.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2017.05.001/

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