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Asymptotic theory for disc-like crystal growth (I) --- Basic state solutions
1. | Department of Mathematics, McGill University, Montreal QC H3A 2K6, Canada |
2. | National Space Development Agency of Japan (NASDA), Tsukuba Space Center, Tsukuba, Japan |
[1] |
Jian-Jun Xu, Junichiro Shimizu. Asymptotic theory for disc-like crystal growth (II): interfacial instability and pattern formation at early stage of growth. Communications on Pure and Applied Analysis, 2004, 3 (3) : 527-543. doi: 10.3934/cpaa.2004.3.527 |
[2] |
Jie Wang, Xiaoqiang Wang. New asymptotic analysis method for phase field models in moving boundary problem with surface tension. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3185-3213. doi: 10.3934/dcdsb.2015.20.3185 |
[3] |
Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 593-608. doi: 10.3934/dcdsb.2010.13.593 |
[4] |
Min Chen, Nghiem V. Nguyen, Shu-Ming Sun. Solitary-wave solutions to Boussinesq systems with large surface tension. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1153-1184. doi: 10.3934/dcds.2010.26.1153 |
[5] |
Samuel Walsh. Steady stratified periodic gravity waves with surface tension II: Global bifurcation. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 3287-3315. doi: 10.3934/dcds.2014.34.3287 |
[6] |
Hyung Ju Hwang, Youngmin Oh, Marco Antonio Fontelos. The vanishing surface tension limit for the Hele-Shaw problem. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3479-3514. doi: 10.3934/dcdsb.2016108 |
[7] |
Calin Iulian Martin. Dispersion relations for periodic water waves with surface tension and discontinuous vorticity. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 3109-3123. doi: 10.3934/dcds.2014.34.3109 |
[8] |
Roman M. Taranets, Jeffrey T. Wong. Existence of weak solutions for particle-laden flow with surface tension. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 4979-4996. doi: 10.3934/dcds.2018217 |
[9] |
Colette Calmelet, Diane Sepich. Surface tension and modeling of cellular intercalation during zebrafish gastrulation. Mathematical Biosciences & Engineering, 2010, 7 (2) : 259-275. doi: 10.3934/mbe.2010.7.259 |
[10] |
Nataliya Vasylyeva, Vitalii Overko. The Hele-Shaw problem with surface tension in the case of subdiffusion. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1941-1974. doi: 10.3934/cpaa.2016023 |
[11] |
Samuel Walsh. Steady stratified periodic gravity waves with surface tension I: Local bifurcation. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 3241-3285. doi: 10.3934/dcds.2014.34.3241 |
[12] |
Xuming Xie. Analytic solution to an interfacial flow with kinetic undercooling in a time-dependent gap Hele-Shaw cell. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4663-4680. doi: 10.3934/dcdsb.2020307 |
[13] |
Stéphane Brull, Bruno Dubroca, Corentin Prigent. A kinetic approach of the bi-temperature Euler model. Kinetic and Related Models, 2020, 13 (1) : 33-61. doi: 10.3934/krm.2020002 |
[14] |
Hung-Wen Kuo. Effect of abrupt change of the wall temperature in the kinetic theory. Kinetic and Related Models, 2019, 12 (4) : 765-789. doi: 10.3934/krm.2019030 |
[15] |
Reiner Henseler, Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez. A kinetic model for grain growth. Kinetic and Related Models, 2008, 1 (4) : 591-617. doi: 10.3934/krm.2008.1.591 |
[16] |
Ming Chen, Meng Fan, Xing Yuan, Huaiping Zhu. Effect of seasonal changing temperature on the growth of phytoplankton. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1091-1117. doi: 10.3934/mbe.2017057 |
[17] |
Rafael Granero-Belinchón, Martina Magliocca. Global existence and decay to equilibrium for some crystal surface models. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2101-2131. doi: 10.3934/dcds.2019088 |
[18] |
Güher Çamliyurt, Igor Kukavica. A local asymptotic expansion for a solution of the Stokes system. Evolution Equations and Control Theory, 2016, 5 (4) : 647-659. doi: 10.3934/eect.2016023 |
[19] |
Thierry Paul, Mario Pulvirenti. Asymptotic expansion of the mean-field approximation. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1891-1921. doi: 10.3934/dcds.2019080 |
[20] |
Kazuo Aoki, Ansgar Jüngel, Peter A. Markowich. Small velocity and finite temperature variations in kinetic relaxation models. Kinetic and Related Models, 2010, 3 (1) : 1-15. doi: 10.3934/krm.2010.3.1 |
2020 Impact Factor: 1.327
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