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We consider a Cahn-Hilliard gradient flow model with a free energy functional, which contains a non-local term in addition to linear and non-linear local terms. The non-local terms can be based on smooth and weakly singular kernel operators. We establish the well-posedness of this problem, construct an unconditional energy stable scheme, and carry out a stability and convergence analysis. Several numerical results are presented to illustrate the efficiency and robustness of the proposed scheme.
}, issn = {3105-2266}, doi = {https://doi.org/10.4208/aam.OA-2025-0004}, url = {http://global-sci.org/intro/article_detail/aam/24148.html} }We consider a Cahn-Hilliard gradient flow model with a free energy functional, which contains a non-local term in addition to linear and non-linear local terms. The non-local terms can be based on smooth and weakly singular kernel operators. We establish the well-posedness of this problem, construct an unconditional energy stable scheme, and carry out a stability and convergence analysis. Several numerical results are presented to illustrate the efficiency and robustness of the proposed scheme.