Citation: Franck Davhys Reval Langa, Armel Judice Ntsokongo. A conserved phase-field model based on type II heat conduction[J]. AIMS Mathematics, 2018, 3(2): 288-297. doi: 10.3934/Math.2018.2.288
| [1] | G. Caginalp, Conserved-phase field system: implications for kinetic undercooling, phys. Rev. B, 38 (1988), 789–791. |
| [2] | G. Caginalp, The dynamics of a conserved phase-field system: Stefan-Like, Hele-Shaw and Cahn- Hilliard models as asymptotic limits, IMA J. Appl. Math., 1 (1990), 77–94. |
| [3] | D. Brochet, D. Hilhorst and A. Novick-Cohen, Maximal attractor and inertial sets for a conserved phase field model, Adv. Differ. Equ-NY, 1 (1996), 547–578. |
| [4] | G. Gilardi, On a conserved phase field model with irregular potentials and dynamic boundary conditions, Istit. Lombardo Accad. Sci. Lett. Rend. A, 14 (2007), 129–161. |
| [5] | C. I. Christov and P. M. Jordan, Heat conduction paradox involving second-sound propagation in moving media, Phys. Rev. Lett., 94 (2005), 154301. |
| [6] | M. Grasselli, A. Miranville, V. Pata, et al. Well-posedness and long time behavior of a parabolichyperbolic phase-field system with singular potentials, Math. Nachr., 280 (2007), 1475–1509. |
| [7] | L. Cherfils, A. Miranville and S. Peng, Higher-order models in phase separation, J. Appl. Anal. Comput., 7 (2017), 39–56. |
| [8] | L. Cherfils, A. Miranville and S. Peng, Higher-order generalized Cahn-Hilliard equations, Electron. J. Qual. Theo., 9 (2017), 1–22. |
| [9] | A. Miranville, Some mathematical models in phase transition, Discrete Cont. Dyn-S, 7 (2014), 271–306. |
| [10] | A. Miranville, On the conserved phase-field model, J. Math. Anal. Appl., 400 (2013), 143–152. |
| [11] | A. Miranville, On higher-order anisotropic conservative Caginalp phase-field systems, Appl. Math. Opt., 77 (2018), 1–18. |
| [12] | A. Miranville and R. Quintanilla, Some generalizations of the Caginalp phase-field system, Appl. Anal., 88 (2009), 877–894. |
| [13] | A. Miranville and R. Quintanilla, A conserved phase-field system based on the Maxwell-Cattaneo law, Nonlinear Anal-Real, 14 (2013), 1680–1692. |
| [14] | A. Miranville and R. Quintanilla, A Caginalp phase-field system based on type Ⅲ heat conduction with two temperatures, Quart. Appl. Math., 74 (2016), 375–398. |
| [15] | A. Miranville and R. Quintanilla, A generalization of the Caginalp phase-field system based on the Cattaneo law, Nonlinear Anal-Theor, 71 (2009), 2278–2290. |
| [16] | A. Miranville and S. Zelik, The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions, Discrete cont. Dyn-A, 28 (2010), 275–310. |
| [17] | A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, In: Handbook of Differential Equations, Evolutionary Partial Differential Equations, C. M. Dafermos, M. Pokorny eds., Elsevier, Amsterdam, 4 (2008), 103–200. |
| [18] | A. Miranville and S. Zelik, Robust exponential attractors for Cahn-Hilliard type equations with singular potentials, Math. Methods Appl. Sci., 27 (2004), 545–582. |
| [19] | J. Jiang, Convergence to equilibrium for a parabolic-hyperbolic phase-field model with Cattaneo heat flux law, J. Math. Anal. Appl., 341 (2008), 149–169. |
| [20] | J. W. Cahn, On spinodal decomposition, Acta Metall., 9 (1961), 795–801. |
| [21] | A. E. Green, P. M. Naghdi, On Undamped heat waves in an elastic solid, J. Therm. Stresses, 15 (1992), 253–264. |
| [22] | A. J. Ntsokongo, D. Moukoko, F. D. R. Langa, et al. On higher-order anisotropic conservative Caginalp phase-field type models, AIMS Mathematics, 2 (2017), 215–229. |
| [23] | A. J. Ntsokongo and N. Batangouna, Existence and uniqueness of solutions for a conserved phasefield type model, AIMS Mathematics, 1 (2016), 144–155. |
| [24] | A. Morro, L. E. Payne and B. Straughan, Decay, growth, continuous dependence and uniqueness results in generalized heat conduction theories, Appl. Anal., 38 (1990), 231–243. |
| [25] | R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Second edition, Applied Mathematical Sciences, vol. 68, Springer-Verlag, New York, 1997. |
Franck Davhys Reval Langa, Armel Judice Ntsokongo. A conserved phase-field model based on type II heat conduction[J]. AIMS Mathematics, 2018, 3(2): 288-297. doi: 10.3934/Math.2018.2.288
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