Phase-field systems with nonlinear coupling and dynamic boundary conditions |
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Authors: | Cecilia Cavaterra Alain Miranville |
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Institution: | a Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, 20133 Milano, Italy b Department of Mathematics, University of Missouri, Columbia, MO 65211, USA c Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, 20133 Milano, Italy d Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086, SP2MI, 86962 Chasseneuil Futuroscope Cedex, France |
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Abstract: | We consider phase-field systems of Caginalp type on a three-dimensional bounded domain. The order parameter fulfills a dynamic boundary condition, while the (relative) temperature is subject to a homogeneous boundary condition of Dirichlet, Neumann or Robin type. Moreover, the two equations are nonlinearly coupled through a quadratic growth function. Here we extend several results which have been proven by some of the authors for the linear coupling. More precisely, we demonstrate the existence and uniqueness of global solutions. Then we analyze the associated dynamical system and we establish the existence of global as well as exponential attractors. We also discuss the convergence of given solutions to a single equilibrium. |
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Keywords: | 35B40 35B41 35K55 80A22 |
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