In this article, we study the existence and uniqueness solution for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms with homogenous Dirichlet boundary conditions, in a bounded smooth domain.
L.Cherfils, S.Gatti and A.Miranville, Exitence and globalsolutions to the Caginalp phase-fields system with dynamic boundary conditions and singular potentials, Vol. 348, 2008, pp. 1029–1030.
2.
B.L.Doumbé Bongola, textitEtude de modèles de champ de phases de type Caginalp. Thèse soutenue à la Faculté des Sciences Fondamentales et Appliquées de Poitiers, le 30 mai 2013.
3.
M.Grasselli, A.Miranville, V.Pata and S.Zelik, Well-posedness and long time behavior of a parabolic-hyperbolic phasefield system with singular potentials, Math. Nachr.280(13–14) (2007), 1475–1509. doi:10.1002/mana.200510560.
4.
A.Miranville and R.Quintanilla, Some generalizations of the Caginalp phase-field system, Vol. 88, 2009, pp. 877–894.
5.
A.Miranville and R.Quintanilla, A generalization of the Caginalp phase-field system based on the Maxwell–Cattaneo law, Nonlinear Anal.71(5–6) (2009), 2278–2298. doi:10.1016/j.na.2009.01.061.
6.
A.Miranville and R.Quintanilla, Some generalizations of the Caginalp phase-field system based on the Cattaneo law, Vol. 71, 2009, pp. 2278–2290.
7.
A.Miranville and R.Quintanilla, A Caginalp phase-field system with nonlinear coupling, Nonlinear Anal. Real World Appl.11 (2010), 2849–2861. doi:10.1016/j.nonrwa.2009.10.008.
8.
A.Miranville and R.Quintanilla, A Caginalp phase-field system based on type III heat conduction with two temperature.
9.
D.Moukoko, Well-posedness and long time behavior of a hyperbolic Caginalp system, JAAC4(2) (2014), 151–196.
10.
D.Moukoko, Etude de modèles hyperboliques de champ de phases de Caginalp, Thèse unique, Faculté des Sciences et Techniques, Université Marien NGOUABI23 janvier (2015).
11.
D.Moukoko, F.Moukamba and F.D.R.Langa, Global Attractor for Caginalp Hyperbolic Field-phase System with Singular Potentiel, Journal of Mathematics Research7(3) (2015). doi:10.5539/jmr.v7n3p165.
12.
C.Wehbe, Etude asymptotique de modèles en transition de phase. Thèse Mathématiques et leurs interactions, 2014.