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Asymptotic theory for disclike 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] 
JianJun Xu, Junichiro Shimizu. Asymptotic theory for disclike crystal growth (II): interfacial instability and pattern formation at early stage of growth. Communications on Pure & Applied Analysis, 2004, 3 (3) : 527543. 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 & Continuous Dynamical Systems  B, 2015, 20 (9) : 31853213. doi: 10.3934/dcdsb.2015.20.3185 
[3] 
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 
[4] 
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 
[5] 
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 
[6] 
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 
[7] 
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 
[8] 
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 
[9] 
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 
[10] 
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 
[11] 
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 
[12] 
Ming Chen, Meng Fan, Xing Yuan, Huaiping Zhu. Effect of seasonal changing temperature on the growth of phytoplankton. Mathematical Biosciences & Engineering, 2017, 14 (56) : 10911117. doi: 10.3934/mbe.2017057 
[13] 
Kazuo Aoki, Ansgar Jüngel, Peter A. Markowich. Small velocity and finite temperature variations in kinetic relaxation models. Kinetic & Related Models, 2010, 3 (1) : 115. doi: 10.3934/krm.2010.3.1 
[14] 
Güher Çamliyurt, Igor Kukavica. A local asymptotic expansion for a solution of the Stokes system. Evolution Equations & Control Theory, 2016, 5 (4) : 647659. doi: 10.3934/eect.2016023 
[15] 
Naoufel Ben Abdallah, Antoine Mellet, Marjolaine Puel. Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach. Kinetic & Related Models, 2011, 4 (4) : 873900. doi: 10.3934/krm.2011.4.873 
[16] 
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 
[17] 
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 
[18] 
P. D. Howell, J. J. Wylie, Huaxiong Huang, Robert M. Miura. Stretching of heated threads with temperaturedependent viscosity: Asymptotic analysis. Discrete & Continuous Dynamical Systems  B, 2007, 7 (3) : 553572. doi: 10.3934/dcdsb.2007.7.553 
[19] 
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 
[20] 
Marissa Condon, Jing Gao, Arieh Iserles. On asymptotic expansion solvers for highly oscillatory semiexplicit DAEs. Discrete & Continuous Dynamical Systems  A, 2016, 36 (9) : 48134837. doi: 10.3934/dcds.2016008 
2016 Impact Factor: 0.994
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