AIMS Mathematics, 2017, 2(2): 215-229. doi: 10.3934/Math.2017.2.215.

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On higher-order anisotropic conservative Caginalp phase-field type models

Faculté des Sciences et Techniques, Université Marien Ngouabi, BP.69 Brazzaville, Congo

Our aim in this paper is to study the well-posedness of higher-order (in space) anisotropic conservative phase-field systems. More precisely, we prove the existence and uniqueness of solutions.
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Keywords Conserved phase-field systems; Higher-order systems; Anisotropy Well-posedness

Citation: Armel Judice Ntsokongo, Daniel Moukoko, Franck Davhys Reval Langa, Fidèle Moukamba. On higher-order anisotropic conservative Caginalp phase-field type models. AIMS Mathematics, 2017, 2(2): 215-229. doi: 10.3934/Math.2017.2.215


  • 1. S. Agmon, Lectures on elliptic boundary value problems, Mathematical Studies. Van Nostrand, New York, 1965.
  • 2. S. Agmon, A. Douglis, L. Nirenberg Estimates near the boundary for solutions of elliptic partial differential equations, I, Commun. Pure Appl. Math., 12 (1959), 623-727.
  • 3. G. Caginalp, Conserved-phase field system: implications for kinetic undercooling, phys. Rev. B, 38 (1988), 789-791.    
  • 4. 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.    
  • 5. G. Caginalp, An analysis of a phase-field model of a free boundary, Arch. Rational Mech. Anal., 92 (1986), 205-245.
  • 6. G. Caginalp and E. Esenturk, Anisotropic phase-field equations of arbitrary order, Discrete Contin. Dyn. Systems S, 4 (2011), 311-350.
  • 7. X. Chen, G. Caginalp and E. Esenturk, Interface conditions for a phase field model with anisotropic and non-local interactions, Arch. Ration. Mech. Anal., 202 (2011), 349-372 .    
  • 8. L. Cherfils, A. Miranville and S.Peng, Higher-order models in phase separation, J. Appl. Anal. Comput., 2017.
  • 9. L. Cherfils, A. Miranville, On the Caginalp system with dynamic boundary conditions and syngular potential, Appl. Math., 54 (2009), 89-115.    
  • 10. H. Fakih, Etude mathmatique et numrique de quelques gnralisations de l'quation de Cahn-Hilliard : Applications la retouche d'images et la biologie, PhD thesis, Universit de Poitiers, 2015.
  • 11. G. Giacomin and J.L. Lebowitz, Phase segregation dynamics in particle systems with long range interaction I. Macroscopic limits, J. Statist. Phys., 87 (1997), 37-61.    
  • 12. H. Israel, Comportement asymptotique de modles en sparation de phase, PhD thesis, Universit de Poitiers, 2013.
  • 13. A. Miranville, R. Quintanilla, A type III phase-field system with a logarithmic potential, Appl. Math. Letters, 24 (2011), 1003-1008.    
  • 14. A. Miranville, R. Quintanilla, A generalization of the Caginalp phase-field system based on the Cattaneo law, Nonlinear. Anal. TMA, 71 (2009), 2278-2290.    
  • 15. A. Miranville, R. Quintanilla, Some generalizations of the Caginalp phase-field system, Appl. Anal., 88 (2009), 877-894.    
  • 16. A. Miranville, Some mathematical models in phase transition, Discrete Contin. Dyn. Systems Series S, 7 (2014), 271-306.
  • 17. A. Miranville On higher-order anisotropic conservative Caginalp phase-field systems,Appl Math Optim, 2016, 1-18.
  • 18. A. Miranville, R. Quintanilla, A Caginalp phase-field system based on type III heat conduction with two temperatures, Quart. Appl. Math., 74 (2016), 375-398.    
  • 19. A. Miranville, On the conserved phase-field model, J. Math. Anal. Appl., 400 (2013), 143-152.    
  • 20. A. Miranville, Higher-order Anisotropic Caginalp Phase-Field systems, Mediterr. J. Math., 2016.
  • 21. A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in Handbook of Di erential Equations, Evolutionary Partial Differential Equations, C.M. Dafermos, M. Pokorny eds., Elsevier, Amsterdam, 4 (2008), 103-200.
  • 22. A.J. Ntsokongo, On higher-order anisotropic Caginalp phase-field systems with polynomial nonlinear terms, J. Appl. Anal. Comput., 2017.
  • 23. A.J. Ntsokongo, N. Batangouna, Existence and uniqueness of solutions for a conserved phase-field type model, AIMS Mathematics, 1 (2016), 144-155.    
  • 24. R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, 68 (1997).
  • 25. R. Quintanilla, A well-posed problem for the three-dual-phase-lag heat conduction, J. Thermal Stresses, 32 (2009), 1270-1278.    


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