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On an Allen-Cahn type integrodifferential equation

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  • An Allen-Cahn type system si transformed into an integraodifferential equation. Results on well-posedness and long time behavior are presented.
    Mathematics Subject Classification: Primary: 75A15; Secondary: 35K55, 35A05, 35B40.


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  • [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.


    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.


    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.


    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.

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