A nonlocal phase field model of viscous Cahn–Hilliard type is considered. This model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The resulting system of differential equations consists of a highly nonlinear parabolic equation coupled to a nonlocal ordinary differential equation, which has singular terms that render the analysis difficult. Some results are presented on the well-posedness and stability of the system as well as on the distributed optimal control problem.

Nonlocal Phase Field Models of Viscous Cahn–Hilliard Type

Colli, Pierluigi
;
Gilardi, Gianni;
2019-01-01

Abstract

A nonlocal phase field model of viscous Cahn–Hilliard type is considered. This model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The resulting system of differential equations consists of a highly nonlinear parabolic equation coupled to a nonlocal ordinary differential equation, which has singular terms that render the analysis difficult. Some results are presented on the well-posedness and stability of the system as well as on the distributed optimal control problem.
2019
978-3-030-33115-3
978-3-030-33116-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1318586
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