Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 146-154.

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We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].
DOI : 10.1051/mmnp/20127212

V. Vougalter 1 ; V. Volpert 2

1 University of Cape Town, Department of Mathematics, Private Bag, Rondebosch 7701, South Africa
2 Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France
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V. Vougalter; V. Volpert. Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 146-154. doi : 10.1051/mmnp/20127212. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127212/

[1] N.D. Alikakos, G. Fusco Comm. Partial Differential Equations 1994 1397 1447

[2] N. Benkirane. Propriété d’indice en théorie Holderienne pour des opérateurs elliptiques dans . CRAS, 307, série I (1988), 577–580.

[3] L.A. Caffarelli, N.E. Muler Arch. Rational Mech. Anal. 1995 129 144

[4] H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon. Schrödinger operators with application to quantum mechanics and global geometry. Springer-Verlag, Berlin, 1987.

[5] A. Ducrot, M. Marion, V. Volpert CRAS 2005 659 664

[6] A. Ducrot, M. Marion, V. Volpert Advances Diff. Equations 2008 1151 1192

[7] P.J. Flory J.Chem.Phys. 1942 51 61

[8] P. Howard Adv. Differential Equations 2009 87 120

[9] B.L.G. Jonsson, M. Merkli, I.M. Sigal, F. Ting. Applied Analysis. In preparation.

[10] T. Kato Math. Ann. 1965 258 279

[11] M.D. Korzec, P.L. Evans, A. Münch, B. Wagner SIAM J. Appl. Math. 2008 348 374

[12] E. Lieb, M. Loss. Analysis. Graduate studies in Mathematics, 14. American Mathematical Society, Providence, 1997.

[13] M. Reed, B. Simon. Methods of Modern Mathematical Physics, III : Scattering Theory, Academic Press, 1979.

[14] I. Rodnianski, W. Schlag Invent. Math. 2004 451 513

[15] T.V. Savina, A.A. Golovin, S.H. Davis, A.A. Nepomnyaschy, P.W.V Oorhees Phys. Rev. E 2003 021606

[16] V.A. Shchukin, D. Bimberg Rev. Modern Phys. 1999 1125 1171

[17] V. Volpert, B. Kazmierczak, M. Massot, Z. Peradzynski Appl. Math. 2002 219 238

[18] V. Vougalter, V. Volpert Proc. Edinb. Math. Soc. (2) 2011 249 271

[19] V. Vougalter, V. Volpert Int. J. Pure Appl. Math. 2010 169 191

[20] V. Vougalter, V. Volpert Commun. Pure Appl. Anal. 2012 365 373

[21] V. Vougalter, V. Volpert Int. Electron. J. Pure Appl.Math. 2010 75 83

[22] V. Volpert, V. Vougalter. On the solvability conditions for a linearized Cahn-Hilliard equation. To appear in Rendiconti dell’Instituto di Matematica dell’Universita di Trieste.

[23] V. Vougalter, V. Volpert Int. Electron. J. Pure Appl.Math. 2010 183 187

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