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2011, 2011(Special): 824-833. doi: 10.3934/proc.2011.2011.824

Global attractor of the multivalued semigroup associated with a phase-field model of grain boundary motion with constraint

1. 

Department of Education, School of Education, Bukkyo University, 96 Kitahananobo-cho, Murasakino, Kita-ku, Kyoto, 603-8301

2. 

Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, 221-8686

Received  July 2010 Revised  August 2010 Published  October 2011

We consider a phase-fi eld model of grain boundary motion with constraint, which is a nonlinear system of Kobayashi-Warren-Carter type: a nonlinear parabolic partial diff erential equation and a nonlinear parabolic variational inequality. Recently the existence of solutions to our system was shown in the N-dimensional case. Also the uniqueness was proved in the case when the space dimensional is one and initial data are good. In this paper we study the asymptotic stability of our model without uniqueness. In fact we shall construct global attractors for multivalued semigroups (multivalued semiflows) associated with our system in the N-dimensional case.
Citation: Nobuyuki Kenmochi, Noriaki Yamazaki. Global attractor of the multivalued semigroup associated with a phase-field model of grain boundary motion with constraint. Conference Publications, 2011, 2011 (Special) : 824-833. doi: 10.3934/proc.2011.2011.824
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