AIMS Mathematics, 2018, 3(2): 263-287. doi: 10.3934/Math.2018.2.263.

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Time periodic solutions of Cahn-Hilliard systems with dynamic boundary conditions

Graduate School of Education, Kyoto University of Education 1 Fujinomori, Fukakusa, Fushimi-ku,Kyoto 612-8522, Japan

The existence problem for Cahn-Hilliard systems with dynamic boundary conditions andtime periodic conditions is discussed. We apply the abstract theory of evolution equations with viscosityapproach and the Schauder fixed point theorem in the level of approximate problems. One ofthe key points is the assumption for maximal monotone graphs with respect to their e ective domains.Thanks to this, we obtain the existence result of periodic solutions by using the passage to the limit.
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Keywords Cahn-Hilliard system; dynamic boundary condition; time periodic solution; perturbation term; growth condition

Citation: Taishi Motoda. Time periodic solutions of Cahn-Hilliard systems with dynamic boundary conditions. AIMS Mathematics, 2018, 3(2): 263-287. doi: 10.3934/Math.2018.2.263

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