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

References

• James RD. Displacive phase transformations in solids. J Mech Phys Solids. 1986;34(4):359–394. doi: 10.1016/0022-5096(86)90008-6
   Web of Science ®Google Scholar
• Meethong N, Kao YH, et al. Electrochemically induced phase transformation in nanoscale olivines Li1−xMPO4(M=Fe,Mn). Chem Mater. 2012;20:6189–6198. doi: 10.1021/cm801722f
   Google Scholar
• Lines ME, Glass AM, Burns G. Principles and applications of ferroelectrics and related materials. Phys Today. 1978;31(9):56–58. doi: 10.1063/1.2995188
   Google Scholar
• Balakrishna AR, Carter WC. Combining phase-field crystal methods with a Cahn–Hilliard model for binary alloys. Phys Rev E. 2018;97(4):043304. doi: 10.1103/PhysRevE.97.043304
   PubMed Web of Science ®Google Scholar
• Balakrishna AR, Chiang YM, Carter WC. Phase-field model for diffusion-induced grain boundary migration: an application to battery electrodes. Phys Rev Mater. 2019;3(6):065404. doi: 10.1103/PhysRevMaterials.3.065404
   Web of Science ®Google Scholar
• Cahn JW, Hilliard JE. Free energy of a nonuniform system: I. interfacial free energy. J Chem Phys. 1958;28(2):258–267. doi: 10.1063/1.1744102
   Web of Science ®Google Scholar
• Elder KR, Katakowski M, et al. Modeling elasticity in crystal growth. Phys Rev Lett. 2002;88(24):245701. doi: 10.1103/PhysRevLett.88.245701
   PubMed Web of Science ®Google Scholar
• Kundin J, Choudhary MA. Application of the anisotropic phase-field crystal model to investigate the lattice systems of different anisotropic parameters and orientations, model. Simul Mater Sci Eng. 2017;25(5):055004. doi: 10.1088/1361-651X/aa6e48
   Web of Science ®Google Scholar
• Prieler R, Hubert J, Li D, et al. An anisotropic phase-field crystal model for heterogeneous nucleation of ellipsoidal colloids. J Phys Condens Matter. 2009;21(46):464110. doi: 10.1088/0953-8984/21/46/464110
   PubMed Web of Science ®Google Scholar
• Chockalingam K, Dörfler W. Implementation of the coupled two-mode phase field crystal model with Cahn–Hilliard for phase-separation in battery electrode particles. Int J Numer Methods Eng. 2021;122(10):2566–2580. doi: 10.1002/nme.v122.10
   Web of Science ®Google Scholar
• Schimperna G, Zelik S. Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Trans Am Math Soc. 2013;365(7):3799–3829. doi: 10.1090/tran/2013-365-07
   Web of Science ®Google Scholar
• Alber H, Zhu P. Solutions to a model for interface motion by interface diffusion. Proc R Soc Edinb: Sect A Math. 2008;138(5):923–955. doi: 10.1017/S0308210507000170
   Google Scholar
• Bernis F, Friedman A. Higher order nonlinear degenerate parabolic equations. J Differ Equ. 1990;83:179–206. doi: 10.1016/0022-0396(90)90074-Y
   Web of Science ®Google Scholar
• Beretta E, Bertsch M, Dal Passo R. Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation. Arch Ration Mech Anal. 1995;129:175–200. doi: 10.1007/BF00379920
   Web of Science ®Google Scholar
• Duan N, Li Z, Liu F. Weak solutions for a sixth-order phase-field equation with degenerate mobility. Bull Malays Math Sci Soc. 2020;43:1857–1883. doi: 10.1007/s40840-019-00777-x
   Web of Science ®Google Scholar
• Dai S, Du Q. Weak solutions for the Cahn–Hilliard equation with degenerate mobility. Arch Ration Mech Anal. 2016;219:1161–1184. doi: 10.1007/s00205-015-0918-2
   Web of Science ®Google Scholar
• Dai S, Liu Q, Promislow K. Weak solutions for the functionalized Cahn–Hilliard equation with degenerate mobility. Applicable Anal. 2021;100(1):1–16. doi: 10.1080/00036811.2019.1585536
   Web of Science ®Google Scholar
• Elliott CM, Garcke H. On the Cahn–Hilliard equation with degenerate mobility. SIAM J Math Anal. 1996;27(2):404–423. doi: 10.1137/S0036141094267662
   Web of Science ®Google Scholar
• Liu C. Sixth-order thin film equation in two space dimensions. Adv Differ Equ. 2015;20(5-6):557–580.
   Web of Science ®Google Scholar
• Yin J. On the existence of nonnegative continuous solutions of the Cahn–Hilliard equation. J Differ Equ. 1992;97(2):310–327. doi: 10.1016/0022-0396(92)90075-X
   Web of Science ®Google Scholar
• Roubíček T. A generalization of the Lions–Temam compact imbedding theorem. Cas Pest Mat. 1990;115(4):338–342.
   Google Scholar
• Lions J. Quelques methodes de resolution des problemes aux limites non lineaires. Paris: Dunod Gauthier-Villars; 1969.
   Google Scholar
• Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer; 1983.
   Google Scholar
• Evans LC, Gariepy RF. Measure theory and fine properties of functions. Boca Raton: CRC Press; 1992.
   Google Scholar