# American Institute of Mathematical Sciences

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

## On an Allen-Cahn type integrodifferential equation

 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.
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.   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.  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.  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.  doi: 10.1007/s11587-006-0008-8.  Google Scholar

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##### 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.   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.  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.  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.  doi: 10.1007/s11587-006-0008-8.  Google Scholar
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