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Twelve limit cycles in a cubic order planar system with $Z_2$- symmetry
Asymptotic theory for disc-like crystal growth (II): interfacial instability and pattern formation at early stage of growth
1. | Department of Mathematics, McGill University, Montreal QC H3A 2K6 |
2. | National Space Development Agency of Japan (NASDA), Tsukuba Space Center, Tsukuba |
[1] |
Jian-Jun Xu, Junichiro Shimizu. Asymptotic theory for disc-like crystal growth (I) --- Basic state solutions. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1091-1116. doi: 10.3934/dcdsb.2004.4.1091 |
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Abed Bounemoura, Edouard Pennamen. Instability for a priori unstable Hamiltonian systems: A dynamical approach. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 753-793. doi: 10.3934/dcds.2012.32.753 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
[13] |
Franz Wirl, Andreas J. Novak. Instability and growth due to adjustment costs. Numerical Algebra, Control and Optimization, 2013, 3 (1) : 63-76. doi: 10.3934/naco.2013.3.63 |
[14] |
Antonin Chambolle, Gilles Thouroude. Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem. Networks and Heterogeneous Media, 2009, 4 (1) : 127-152. doi: 10.3934/nhm.2009.4.127 |
[15] |
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 |
[16] |
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 |
[17] |
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 |
[18] |
Shengfu Deng. Generalized pitchfork bifurcation on a two-dimensional gaseous star with self-gravity and surface tension. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3419-3435. doi: 10.3934/dcds.2014.34.3419 |
[19] |
Marcelo M. Disconzi, Igor Kukavica. A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid. Evolution Equations and Control Theory, 2019, 8 (3) : 503-542. doi: 10.3934/eect.2019025 |
[20] |
Grigor Nika, Bogdan Vernescu. Rate of convergence for a multi-scale model of dilute emulsions with non-uniform surface tension. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1553-1564. doi: 10.3934/dcdss.2016062 |
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