Affiliations: Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Milano, Italy. E-mails: monica.conti@polimi.it, filippo.delloro@mail.polimi.it | Laboratoire de Mathématiques et Applications, Université de Poitiers, Chasseneuil Futuroscope Cedex, France. E-mail: Alain.Miranville@math.univ-poitiers.fr
Note: [] Corresponding author: Monica Conti, Politecnico di Milano, Dipartimento di Matematica “F. Brioschi”, Via Bonardi 9, I-20133 Milano, Italy. E-mail: monica.conti@polimi.it
Abstract: We discuss the asymptotic behavior of a generalized nonlinear Caginalp phase-field system, based on the theory of heat conduction of type III devised by Green and Naghdi. In the case of two nonlinearities of polynomial critical growth, we prove the existence of global attractors of optimal regularity.
Keywords: Caginalp system, type III heat conduction, well-posedness, dissipativity, global attractor
