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June  2013, 6(3): 703-709. doi: 10.3934/dcdss.2013.6.703

On an Allen-Cahn type integrodifferential equation

Gianni Gilardi 1,

1. 

Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia

Received  April 2010 Revised  January 2011 Published  December 2012

An Allen-Cahn type system si transformed into an integraodifferential equation. Results on well-posedness and long time behavior are presented.
Keywords: Allen-Cahn equation, long-time behavior., integrodifferential equations, well posedness.
Mathematics Subject Classification: Primary: 75A15; Secondary: 35K55, 35A05, 35B4.
Citation: Gianni Gilardi. On an Allen-Cahn type integrodifferential equation. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 703-709. doi: 10.3934/dcdss.2013.6.703
References:
[1]

S. M. Allen and J. W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metallurgica, 27 (1979), 1085-1095. Google Scholar

[2]

P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, Global solution and long-time behavior for a problem of phase segregation of the Allen-Cahn type, $M^3AS$ Math. Models Methods Appl. Sci., 20 (2010), 519-541. doi: 10.1142/S0218202510004325.  Google Scholar

[3]

M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Phys. D, 92 (1996), 178-192. doi: 10.1016/0167-2789(95)00173-5.  Google Scholar

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P. Podio-Guidugli, Models of phase segregation and diffusion of atomic species on a lattice, Ric. Mat., 55 (2006), 105-118. doi: 10.1007/s11587-006-0008-8.  Google Scholar

show all references

References:
[1]

S. M. Allen and J. W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metallurgica, 27 (1979), 1085-1095. Google Scholar

[2]

P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, Global solution and long-time behavior for a problem of phase segregation of the Allen-Cahn type, $M^3AS$ Math. Models Methods Appl. Sci., 20 (2010), 519-541. doi: 10.1142/S0218202510004325.  Google Scholar

[3]

M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Phys. D, 92 (1996), 178-192. doi: 10.1016/0167-2789(95)00173-5.  Google Scholar

[4]

P. Podio-Guidugli, Models of phase segregation and diffusion of atomic species on a lattice, Ric. Mat., 55 (2006), 105-118. doi: 10.1007/s11587-006-0008-8.  Google Scholar

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