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AIMS Mathematics

2016, Volume 1, Issue 2: 144-155. doi: 10.3934/Math.2016.2.144
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Research article

Existence and uniqueness of solutions for a conserved phase-field type model

  • Facult´e des Sciences et Techniques, Universit´e Marien Ngouabi, BP.69 Brazzaville, Congo
  • Received: 14 July 2016 Accepted: 25 July 2016 Published: 02 August 2016

  • In this paper, we study the existence and the uniqueness of solutions of a conserved phasefield model in a bounded and smooth domain.

    Citation: Armel Judice Ntsokongo, Narcisse Batangouna. Existence and uniqueness of solutions for a conserved phase-field type model[J]. AIMS Mathematics, 2016, 1(2): 144-155. doi: 10.3934/Math.2016.2.144

    Related Papers:

  • In this paper, we study the existence and the uniqueness of solutions of a conserved phasefield model in a bounded and smooth domain.


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    [1] G. Caginalp, Conserved-phase field system: implications for kinetic undercooling, phys. Rev. B 38 (1988), 789-791.
    [2] G. Caginalp, The dynamics of conseved phase-field system: Stefan-Like, Hele-Shaw and Cahn- Hilliard models as asymptotic limits, IMA J. Appl. Math. 44 (1990), 77-94.
    [3] A. Miranville, On the conserved phase-field model, J. Math. Anal. Appl. 400 (2013), 143-152. 4. A.E. Green, P.M. Naghdi, A re-examination of the basic postulates for thermomechanics, Proc. Royal Society London A 432 (1991), 171-194.
    [4] 5. P. Colli, G. Ggilardi, Ph. Laurenot, and A. Novick-Cohen, uniqueness and long-time behavior for the conserved phase-field system memory, Discrete contin. Dyn. Syst. 5 (1999), 375-390.
    [5] 6. D. Moukoko, Well-posedness and long time behavior of a hyperbolic Caginal phase-field system, Appl. Anal. Comp. 4 (2014), 1-196.
    [6] 7. L. Cherfils, A. Miranville, On the Caginalp system with dynamic boundary conditions and syngular potential, Appl. Math. 54 (2009), 89-115.
    [7] 8. A. Miranville, R. Quintanilla, A type III phase-field system with a logarithmic potential, Appl. Math. Letters 24 (2011), 1003-1008.
    [8] 9. A. Miranville, R. Quintanilla, A generalization of the Caginalp phase-field system based on the Cattaneo law, Nonlinear. Anal. TMA 71 (2009), 2272290.
    [9] 10. B. Doumbe, Etude de modeles de champ de phase de type Caginalp, PhD thesis, Universit de Poiters, 2013.
    [10] 11. R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Second edition, Applied Mathematical Sciences, vol. 68, Springer-Verlag, New York, 1997.
    [11] 12. A. Miranville, R. Quintanilla, Some generalizations of the Caginalp phase-field system, Appl. Anal. 88 (2009), 877-894.
    [12] 13. G. Caginalp, An analysis of a phase-field model of a free boundary, Arch. Rational Mech. Anal. 92 (1986), 205-245.
    [13] 14. R. Quintanilla, A well-posed problem for the three-dual-phase-lag heat conduction, J. Thermal Stresses 32 (2009), 1270-1278.
    [14] 15. A. Miranville, Some mathematical models in phase transition, Discrete Contin. Dyn. Systems Series S 7 (20, 271-306.
    [15] 16. P. J. Chen, M. E. Gurtin, andW.O.Williams, A note on non-simple heat conduction, J. Appl. Phys. (ZAMP) 19 (1968), 969-970.
    [16] 17. A. Miranville, R. Quintanilla, A Caginalp phase-field system based on type III heat conduction with two temperatures, Quart. Appl. Math. 74 (20, 375-398
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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