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Grain sizes in the discrete AllenCahn and CahnHilliard equations
1.  Department of Mathematics, Brigham Young University, Provo, UT 84602, United States 
[1] 
Georgia Karali, Yuko Nagase. On the existence of solution for a CahnHilliard/AllenCahn equation. Discrete & Continuous Dynamical Systems  S, 2014, 7 (1) : 127137. doi: 10.3934/dcdss.2014.7.127 
[2] 
Jie Shen, Xiaofeng Yang. Numerical approximations of AllenCahn and CahnHilliard equations. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 16691691. doi: 10.3934/dcds.2010.28.1669 
[3] 
Alain Miranville, Wafa Saoud, Raafat Talhouk. On the CahnHilliard/AllenCahn equations with singular potentials. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 36333651. doi: 10.3934/dcdsb.2018308 
[4] 
Changchun Liu, Hui Tang. Existence of periodic solution for a CahnHilliard/AllenCahn equation in two space dimensions. Evolution Equations & Control Theory, 2017, 6 (2) : 219237. doi: 10.3934/eect.2017012 
[5] 
Cristina Pocci. On singular limit of a nonlinear $p$order equation related to CahnHilliard and AllenCahn evolutions. Evolution Equations & Control Theory, 2013, 2 (3) : 517530. doi: 10.3934/eect.2013.2.517 
[6] 
Quan Wang, Dongming Yan. On the stability and transition of the CahnHilliard/AllenCahn system. Discrete & Continuous Dynamical Systems  B, 2020, 25 (7) : 26072620. doi: 10.3934/dcdsb.2020024 
[7] 
Alain Miranville, Ramon Quintanilla, Wafa Saoud. Asymptotic behavior of a CahnHilliard/AllenCahn system with temperature. Communications on Pure & Applied Analysis, 2020, 19 (4) : 22572288. doi: 10.3934/cpaa.2020099 
[8] 
Shixing Li, Dongming Yan. On the steady state bifurcation of the CahnHilliard/AllenCahn system. Discrete & Continuous Dynamical Systems  B, 2019, 24 (7) : 30773088. doi: 10.3934/dcdsb.2018301 
[9] 
Juan Wen, Yaling He, Yinnian He, Kun Wang. Stabilized finite element methods based on multiscale enrichment for AllenCahn and CahnHilliard equations. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2021074 
[10] 
Gianni Gilardi. On an AllenCahn type integrodifferential equation. Discrete & Continuous Dynamical Systems  S, 2013, 6 (3) : 703709. doi: 10.3934/dcdss.2013.6.703 
[11] 
Irena Pawłow. Thermodynamically consistent CahnHilliard and AllenCahn models in elastic solids. Discrete & Continuous Dynamical Systems, 2006, 15 (4) : 11691191. doi: 10.3934/dcds.2006.15.1169 
[12] 
Ahmad Makki, Alain Miranville. Existence of solutions for anisotropic CahnHilliard and AllenCahn systems in higher space dimensions. Discrete & Continuous Dynamical Systems  S, 2016, 9 (3) : 759775. doi: 10.3934/dcdss.2016027 
[13] 
Mia Jukić, Hermen Jan Hupkes. Dynamics of curved travelling fronts for the discrete AllenCahn equation on a twodimensional lattice. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 31633209. doi: 10.3934/dcds.2020402 
[14] 
Desheng Li, Xuewei Ju. On dynamical behavior of viscous CahnHilliard equation. Discrete & Continuous Dynamical Systems, 2012, 32 (6) : 22072221. doi: 10.3934/dcds.2012.32.2207 
[15] 
Laurence Cherfils, Alain Miranville, Sergey Zelik. On a generalized CahnHilliard equation with biological applications. Discrete & Continuous Dynamical Systems  B, 2014, 19 (7) : 20132026. doi: 10.3934/dcdsb.2014.19.2013 
[16] 
Álvaro Hernández, Michał Kowalczyk. Rotationally symmetric solutions to the CahnHilliard equation. Discrete & Continuous Dynamical Systems, 2017, 37 (2) : 801827. doi: 10.3934/dcds.2017033 
[17] 
Hongmei Cheng, Rong Yuan. Multidimensional stability of disturbed pyramidal traveling fronts in the AllenCahn equation. Discrete & Continuous Dynamical Systems  B, 2015, 20 (4) : 10151029. doi: 10.3934/dcdsb.2015.20.1015 
[18] 
Murat Uzunca, Ayşe SarıaydınFilibelioǧlu. Adaptive discontinuous galerkin finite elements for advective AllenCahn equation. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 269281. doi: 10.3934/naco.2020025 
[19] 
Tatsuki Mori, Kousuke Kuto, Tohru Tsujikawa, Shoji Yotsutani. Representation formulas of solutions and bifurcation sheets to a nonlocal AllenCahn equation. Discrete & Continuous Dynamical Systems, 2020, 40 (8) : 49074925. doi: 10.3934/dcds.2020205 
[20] 
Xinlong Feng, Huailing Song, Tao Tang, Jiang Yang. Nonlinear stability of the implicitexplicit methods for the AllenCahn equation. Inverse Problems & Imaging, 2013, 7 (3) : 679695. doi: 10.3934/ipi.2013.7.679 
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