Abstract
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.
Acknowledgments
The authors wish to thank the anonymous reviewers for their careful reading and providing invaluable suggestions. The authors would like to sincerely appreciate Prof. Peicheng Zhu for his careful instruction.
Disclosure statement
No potential conflict of interest was reported by the author(s).