Solutions to a coupled Cahn-Hilliard-phase-field-crystal model for grain boundary motion

In this paper, we consider an initial-boundary value problem (IBVP) of a coupled Cahn-Hilliard-phase-field-crystal (CH-PFC) system subject to homogeneous Neumann boundary conditions in one spatial dimension. This CH-PFC model couples the composition field of a diffusing species with the crystallogra...

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Published inApplicable analysis Vol. 103; no. 17; pp. 3160 - 3181
Main Authors Wu, Fan, Yang, Manman, Ma, Li
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 21.11.2024
Taylor & Francis Ltd
Subjects
Boundary conditions
Boundary value problems
Crystallography
degenerate mobility
Galerkin method
Grain boundary migration
higher order parabolic equations
Species diffusion
Weak solutions
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Summary:In this paper, we consider an initial-boundary value problem (IBVP) of a coupled Cahn-Hilliard-phase-field-crystal (CH-PFC) system subject to homogeneous Neumann boundary conditions in one spatial dimension. This CH-PFC model couples the composition field of a diffusing species with the crystallographic and can be used to model the diffusion-induced grain boundary migration in crystalline materials. Under suitable assumptions on the coefficients and initial data, we prove that the IBVP possesses a global weak solution. Our existence proof, which contributes to the verification of the model, is only valid in one space dimension.
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content type line 14
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2024.2344834