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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] 
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] 
Min Chen, Nghiem V. Nguyen, ShuMing Sun. Solitarywave solutions to Boussinesq systems with large surface tension. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 11531184. doi: 10.3934/dcds.2010.26.1153 
[5] 
Samuel Walsh. Steady stratified periodic gravity waves with surface tension II: Global bifurcation. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 32873315. doi: 10.3934/dcds.2014.34.3287 
[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 
[7] 
Calin Iulian Martin. Dispersion relations for periodic water waves with surface tension and discontinuous vorticity. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 31093123. doi: 10.3934/dcds.2014.34.3109 
[8] 
Roman M. Taranets, Jeffrey T. Wong. Existence of weak solutions for particleladen flow with surface tension. Discrete & Continuous Dynamical Systems, 2018, 38 (10) : 49794996. 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) : 259275. doi: 10.3934/mbe.2010.7.259 
[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, 2014, 34 (8) : 32413285. doi: 10.3934/dcds.2014.34.3241 
[12] 
Xuming Xie. Analytic solution to an interfacial flow with kinetic undercooling in a timedependent gap HeleShaw cell. Discrete & Continuous Dynamical Systems  B, 2021, 26 (9) : 46634680. doi: 10.3934/dcdsb.2020307 
[13] 
Stéphane Brull, Bruno Dubroca, Corentin Prigent. A kinetic approach of the bitemperature Euler model. Kinetic & Related Models, 2020, 13 (1) : 3361. doi: 10.3934/krm.2020002 
[14] 
HungWen Kuo. Effect of abrupt change of the wall temperature in the kinetic theory. Kinetic & Related Models, 2019, 12 (4) : 765789. doi: 10.3934/krm.2019030 
[15] 
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 
[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) : 10911117. doi: 10.3934/mbe.2017057 
[17] 
Rafael GraneroBelinchón, Martina Magliocca. Global existence and decay to equilibrium for some crystal surface models. Discrete & Continuous Dynamical Systems, 2019, 39 (4) : 21012131. doi: 10.3934/dcds.2019088 
[18] 
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 
[19] 
Thierry Paul, Mario Pulvirenti. Asymptotic expansion of the meanfield approximation. Discrete & Continuous Dynamical Systems, 2019, 39 (4) : 18911921. doi: 10.3934/dcds.2019080 
[20] 
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 
2020 Impact Factor: 1.327
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