Existence and uniqueness of solution for Cahn-Hilliard hyperbolic phase field system with Dirichlet boundary conditions and polynomial potential


  • A. J. Bissouesse Université Marien Ngouabi
  • Daniel Moukoko Université Marien Ngouabi
  • Franck Langa Université Marien Ngouabi Faculté des Sciences et Techniques
  • Macaire Batchi Université Marien Ngouabi






Cahn-Hilliard hyperbolic phase-field system, polynomial potential, Dirichlet boundary conditions.


Our aim in this article is to study the existence and the uniqueness of solution for Cahn-Hilliard hyperbolic phase-field system, with initial conditions, homogeneous Dirichlet boundary conditions, polynomial potential in a bounded and smooth domain.


[1] Brochet,D., Hilhorst, D. and Novick-Cohen, A., Maximal Attractor and Inertial Sets. for a conserved Phase-Field Model, Advance in Differential Equations, No.1, (1996), pp. 547-578.

[2] Brochet, D., Maximal Attractor and Inertial Sets for Somme Second and Fourth Order Phase-Field Models, In:Pitman Res. Notes Math. Ser, Vol. 296, Longman Sci.Tech,Harloww, (1993), pp. 77-85.

[3] Boukhatem, Benattou, B., and Bita, R., Méthode de faedo-Galerkin pour un probleme aux limites non linéaire. Anale Universitatii Oradea Fasc, Matematica, Tom, XVI (2009), pp. 167-181.

[4] Caginalp, G., The Dynamic of Conserved phase System:Stefan- Like, Heleshaw and Cahn-Hilliard Models as Asymptotic Limits. IMA Journal of Applied Mathematics, No. 44, (1990), pp. 77-94.

[5] Caginalp, G., Conserved-phase Field System:Implications for Kinetic Under cooling. Physical Review B, (1988), pp. 789-791. htt://doxdoi.org/10.1103/physRev B. 38. 789.

[6] Choquet-Bruhat, Y., Dewitt-Morete, C. and Dillard-Bleick, M., Analysis, Manifolds and physics. North-Holland Publishing Company, Amsterdam, New york, Oxford (1977).

[7] Colli, P., Gilardi., Grasseli, M., and Schimperna, G., The Conserved Phase-Field System Wih Momory. Adv.Math.Sci App, No. 11, (2001), pp. 265-291.

[8] Colli, P. , Gilardi, G., Laurenot, ph., and Novick-Cohen, A., Uniqueness and Long-Time Behavior for the Conserved phase-System Memory. Discrete and Continuous Dynamical Systems-Series A, No. 5, (1999), pp. 375-390. http://dx.doi.org/10.3934/dcds.1999.5.375.

[9] Gatti, S., and Pata, V., Exponential Atractor for a Conserved Phase- Field System with Memory. Physica D.Nonlinear Phenomena, No. 189, (2004), pp. 31-48. http:// dx.doi.org/10.16/j.physd.2003.10.005.

[10] Gilardi, G., On a Conserved Phase-Field Model with Irregular Potenials and Dynamic Boundary Condition. Istit. Lombardo.Accad.Sci.Lett.Rend.A, No. 141, (2007), pp. 129-161.

[11] Goyaud, M. E. I., Moukamba, F., Moukoko, D., and Langa, F. D. R. , Existence and Uniqueness of Solution for Caginalp Hyperbolic phase-Field System with polynomial Growth potential. International Mathematical Forum, No. 10, (2015), pp. 477-486.

[12] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non lineaires. Paris, Dunod, (1969).

[13] Mangoubi, J., Moukoko, D., Moukamba, F., and Langa, F. D. R.,(2016). Existence and Uniqueness of solution for Cahn-Hilliard Hyperbolic phase-Field System with Dirichlet Boundary Condition and regular potentials. Applied Mathematics, No. 7, (2016), pp. 2152-7385.

[14] Mavoungou, U., Moukamba, F., Moukoko, D., and Langa, F. D. R., Existence and uniqueness of solution for Caginalp Hyperbolic phase Field System with a singular potential. Nonlinear Analysis and Eq, Vol. 4, No. 4, (2016), pp. 151-160, HIKARI Ltd,www.m-hikari.com.

[15] Miranville, A., On the Conserved Phase-Field Model. Journal of Mathemaical Analysis and Applications, No. 400, (2013), pp. 143-152.

[16] Miranville, A., and Quintanilla, R., A Type III phase -Field System with a Logarithmic potential. Applied Mathematics Letters,No. 24, (2011), pp. 1003-1008.

[17] Moukoko, D., Well-posedness and Longtine Behaviors of a Hyperbolic Caginalp System. Journal of Applied Analysis and Computation, No. 4, (2014), pp. 151-196.

[18] Moukoko, D., Moukamba, F., and Langa, F. D. R., Global Attractor for Caginalp Hyperbolic Field-phase System with Singular potential. Journal of Mathematics Research, No. 7, (2015), pp. 165-177.

[19] Ntsokongo, A. J., and Batangouna, N., Existence and Uniqueness of solutions for a Conserved phase -Field Type model. AIMS Mathematics, No. 1, (2016), pp. 144-145.

View Full Article:

Additional Files