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AIMS Mathematics

2018, Volume 3, Issue 2: 263-287. doi: 10.3934/Math.2018.2.263
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Research article

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
  • Received: 20 February 2018 Accepted: 03 April 2018 Published: 25 May 2018

  • MSC : 35K25, 35A01, 35B10, 35D30

  • The existence problem for Cahn-Hilliard systems with dynamic boundary conditions and time periodic conditions is discussed. We apply the abstract theory of evolution equations with viscosity approach and the Schauder fixed point theorem in the level of approximate problems. One of the 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.

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

    Related Papers:

  • The existence problem for Cahn-Hilliard systems with dynamic boundary conditions and time periodic conditions is discussed. We apply the abstract theory of evolution equations with viscosity approach and the Schauder fixed point theorem in the level of approximate problems. One of the 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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    © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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