We study the longtime behavior of the Caginalp phase-field model with a logarithmic potential and dynamic boundary conditions both for the order parameter and the temperature. Due to the possible lack of distributional solutions, we deal with a suitable definition of solutions based on variational inequalities, for which we prove well-posedness and the existence of global and exponential attractors with finite fractal dimension.
Attractors for a Caginalp model with a logarithmic potential and coupled dynamic boundary conditions / M., Conti; Gatti, Stefania; A., Miranville. - In: ANALYSIS AND APPLICATIONS. - ISSN 0219-5305. - STAMPA. - 11:6(2013), pp. 11-21. [10.1142/S0219530513500243]
Attractors for a Caginalp model with a logarithmic potential and coupled dynamic boundary conditions
GATTI, Stefania;
2013
Abstract
We study the longtime behavior of the Caginalp phase-field model with a logarithmic potential and dynamic boundary conditions both for the order parameter and the temperature. Due to the possible lack of distributional solutions, we deal with a suitable definition of solutions based on variational inequalities, for which we prove well-posedness and the existence of global and exponential attractors with finite fractal dimension.
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