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Twelve limit cycles in a cubic order planar system with $Z_2$ symmetry
Asymptotic theory for disclike 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] 
JianJun Xu, Junichiro Shimizu. Asymptotic theory for disclike crystal growth (I)  Basic state solutions. Discrete & Continuous Dynamical Systems  B, 2004, 4 (4) : 10911116. doi: 10.3934/dcdsb.2004.4.1091 
[2] 
Abed Bounemoura, Edouard Pennamen. Instability for a priori unstable Hamiltonian systems: A dynamical approach. Discrete & Continuous Dynamical Systems  A, 2012, 32 (3) : 753793. doi: 10.3934/dcds.2012.32.753 
[3] 
Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete & Continuous Dynamical Systems  B, 2010, 13 (3) : 593608. doi: 10.3934/dcdsb.2010.13.593 
[4] 
Samuel Walsh. Steady stratified periodic gravity waves with surface tension II: Global bifurcation. Discrete & Continuous Dynamical Systems  A, 2014, 34 (8) : 32873315. doi: 10.3934/dcds.2014.34.3287 
[5] 
Min Chen, Nghiem V. Nguyen, ShuMing Sun. Solitarywave solutions to Boussinesq systems with large surface tension. Discrete & Continuous Dynamical Systems  A, 2010, 26 (4) : 11531184. doi: 10.3934/dcds.2010.26.1153 
[6] 
Hyung Ju Hwang, Youngmin Oh, Marco Antonio Fontelos. The vanishing surface tension limit for the HeleShaw problem. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 34793514. 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 & Continuous Dynamical Systems  A, 2014, 34 (8) : 31093123. doi: 10.3934/dcds.2014.34.3109 
[8] 
Colette Calmelet, Diane Sepich. Surface tension and modeling of cellular intercalation during zebrafish gastrulation. Mathematical Biosciences & Engineering, 2010, 7 (2) : 259275. doi: 10.3934/mbe.2010.7.259 
[9] 
Roman M. Taranets, Jeffrey T. Wong. Existence of weak solutions for particleladen flow with surface tension. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 49794996. doi: 10.3934/dcds.2018217 
[10] 
Nataliya Vasylyeva, Vitalii Overko. The HeleShaw problem with surface tension in the case of subdiffusion. Communications on Pure & Applied Analysis, 2016, 15 (5) : 19411974. doi: 10.3934/cpaa.2016023 
[11] 
Samuel Walsh. Steady stratified periodic gravity waves with surface tension I: Local bifurcation. Discrete & Continuous Dynamical Systems  A, 2014, 34 (8) : 32413285. doi: 10.3934/dcds.2014.34.3241 
[12] 
Franz Wirl, Andreas J. Novak. Instability and growth due to adjustment costs. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 6376. doi: 10.3934/naco.2013.3.63 
[13] 
Reiner Henseler, Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez. A kinetic model for grain growth. Kinetic & Related Models, 2008, 1 (4) : 591617. doi: 10.3934/krm.2008.1.591 
[14] 
Antonin Chambolle, Gilles Thouroude. Homogenization of interfacial energies and construction of planelike minimizers in periodic media through a cell problem. Networks & Heterogeneous Media, 2009, 4 (1) : 127152. doi: 10.3934/nhm.2009.4.127 
[15] 
Rafael GraneroBelinchón, Martina Magliocca. Global existence and decay to equilibrium for some crystal surface models. Discrete & Continuous Dynamical Systems  A, 2019, 39 (4) : 21012131. doi: 10.3934/dcds.2019088 
[16] 
Jie Wang, Xiaoqiang Wang. New asymptotic analysis method for phase field models in moving boundary problem with surface tension. Discrete & Continuous Dynamical Systems  B, 2015, 20 (9) : 31853213. doi: 10.3934/dcdsb.2015.20.3185 
[17] 
Shengfu Deng. Generalized pitchfork bifurcation on a twodimensional gaseous star with selfgravity and surface tension. Discrete & Continuous Dynamical Systems  A, 2014, 34 (9) : 34193435. doi: 10.3934/dcds.2014.34.3419 
[18] 
Grigor Nika, Bogdan Vernescu. Rate of convergence for a multiscale model of dilute emulsions with nonuniform surface tension. Discrete & Continuous Dynamical Systems  S, 2016, 9 (5) : 15531564. doi: 10.3934/dcdss.2016062 
[19] 
Marcelo M. Disconzi, Igor Kukavica. A priori estimates for the 3D compressible freeboundary Euler equations with surface tension in the case of a liquid. Evolution Equations & Control Theory, 2019, 8 (3) : 503542. doi: 10.3934/eect.2019025 
[20] 
Weiqing Xie. A free boundary problem arising from the process of Czochralski crystal growth. Conference Publications, 2001, 2001 (Special) : 380385. doi: 10.3934/proc.2001.2001.380 
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