This paper is devoted to the study of the well-posedness and the long time behavior of the Caginalpphase-field model with singular potentials and dynamic boundary conditions.Thanks to a suitable definition of solutions, coinciding with the strong ones underproper assumptions on the bulk and surfacepotentials, we are able to get dissipative estimates, leading tothe existence of the global attractor with finite fractal dimension,as well as of an exponential attractor.
Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions / L., Cherfils; Gatti, Stefania; A., Miranville. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 11:(2012), pp. 2261-2290. [10.3934/cpaa.2012.11.2261]
Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions
GATTI, Stefania;
2012
Abstract
This paper is devoted to the study of the well-posedness and the long time behavior of the Caginalpphase-field model with singular potentials and dynamic boundary conditions.Thanks to a suitable definition of solutions, coinciding with the strong ones underproper assumptions on the bulk and surfacepotentials, we are able to get dissipative estimates, leading tothe existence of the global attractor with finite fractal dimension,as well as of an exponential attractor.
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1534-0392_2012_6_2261.pdf
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