Data di Pubblicazione:
2010
Citazione:
Phase-field systems with nonlinear coupling and dynamic boundary conditions / C. Cavaterra, C. Gal, M. Grasselli, A. Miranville. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 72:5(2010 Mar), pp. 2375-2399.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Łojasiewicz-Simon inequality; Convergence to equilibrium; Dynamic boundary conditions; Exponential attractors; Global attractors; Laplace-Beltrami operator; Phase-field equations
Elenco autori:
C. Cavaterra, C. Gal, M. Grasselli, A. Miranville
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