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Periodic solutions to the Cahn–Hilliard equation with constraint
Author(s) -
Wang Yifu,
Zheng Jiashan
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3506
Subject(s) - mathematics , constraint (computer aided design) , fixed point theorem , cahn–hilliard equation , operator (biology) , limit (mathematics) , mathematical analysis , viscosity solution , subderivative , schauder fixed point theorem , viscosity , partial differential equation , picard–lindelöf theorem , regular polygon , biochemistry , chemistry , physics , geometry , repressor , convex optimization , quantum mechanics , transcription factor , gene
This paper is concerned with the multidimensional Cahn–Hilliard equation with a constraint. The existence of periodic solutions of the problem is mainly proved under consideration by the viscosity approach. More precisely, with the help of the subdifferential operator theory and Schauder fixed point theorem, the existence of solutions to the approximation of the original problem is shown, and then the solution is obtained by using a passage‐to‐limit procedure based on a prior estimate. Copyright © 2015 John Wiley & Sons, Ltd.