Existence of Solution to Initial-Boundary Value Problems of the Cahn-Hilliard Equation with Nonlocal Terms

Guilan Liu


In this paper, inspired from the study on denoising, segmentation and reconstruction in image processing, and combining
with the theories of two phase flows, we introduce one class of initial-boundary value problem of the Cahn-Hilliard
equation with nonlocal terms. Then, by using the Schauder fixed point theorem, we obtain the existence of weak solutions
to this initial boundary value problem for the nonlocal Cahn-Hilliard equation.

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DOI: https://doi.org/10.5539/jmr.v1n2p179

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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