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### Convergence to equilibrium for the equation and dynamic boundary condition of Cahn-Hilliard type and related topics

##### Prof. Takeshi Fukao, Kyoto University of Education. Sala conferenze IMATI-CNR, Pavia - Wednesday, February 13, 2019 h.15:00

Abstract. In this talk we concerned with the long time behavior of the solution to an equation and dynamic boundary condition of Cahn-Hilliard type with the logarithmic potential. This system is constructed by Cahn-Hilliard system in the bulk and on the boundary, and has a structure of the total mass conservation, namely the volume in the bulk plus the boundary. Firstly we obtain the regularity results and then we can prove the separation property from pure phase. Secondly, we discuss the characterization of the $\omega$-limit set, namely subsequence convergence to a stationary solution. Finally, by applying the extended Lojasiewicz-Simon inequality we can prove that the $\omega$-limit set consists only one point.
This study is joint work with Hao Wu (Fudan University, China).

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