Articoli
Volume 146 • (2012) Rendiconti - Classe di Scienze Matematiche e Naturali
https://doi.org/10.4081/scie.2012.138
FINITE-DIMENSIONAL GLOBAL ATTRACTOR FOR A NONLOCAL PHASE-FIELD SYSTEM
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All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.
Ricevuto: 20 maggio 2015
Pubblicato: 30 dicembre 2012
Pubblicato: 30 dicembre 2012
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We analyze a phase-field system where the energy balance equation is lin-early coupled with a nonlinear and nonlocal ODE for the order parameter χ. The latter equation is characterized by a space convolution term which models long-range inter-actions and a singular configuration potential that forces χ to take values in the interval (−1, 1). We prove that the corresponding dynamical system is dissipative, i.e., it has a bounded absorbing set in a suitable phase space. Then we establish the existence of a finite-dimensional global attractor.
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Come citare
FINITE-DIMENSIONAL GLOBAL ATTRACTOR FOR A NONLOCAL PHASE-FIELD SYSTEM. (2012). Istituto Lombardo - Accademia di Scienze e Lettere - Rendiconti di Scienze, 146. https://doi.org/10.4081/scie.2012.138