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On the stability of periodic solutions in the perturbed chemostat
A finite element method for growth in biological development
1. | Laboratoire de Mathématiques, Informatique et Applications, Université de Haute-Alsace, 4, rue des Frères Lumière, 68093 MULHOUSE Cedex, France |
2. | Department of Physics, Emory University, Maths/Science Center, 400 Dowman Drive, Atlanta, GA 30322 |
[1] |
Roman M. Taranets, Jeffrey T. Wong. Existence of weak solutions for particle-laden flow with surface tension. Discrete & Continuous Dynamical Systems, 2018, 38 (10) : 4979-4996. doi: 10.3934/dcds.2018217 |
[2] |
Alex Bihlo, James Jackaman, Francis Valiquette. On the development of symmetry-preserving finite element schemes for ordinary differential equations. Journal of Computational Dynamics, 2020, 7 (2) : 339-368. doi: 10.3934/jcd.2020014 |
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Zhangxin Chen. On the control volume finite element methods and their applications to multiphase flow. Networks & Heterogeneous Media, 2006, 1 (4) : 689-706. doi: 10.3934/nhm.2006.1.689 |
[4] |
Bin Wang, Lin Mu. Viscosity robust weak Galerkin finite element methods for Stokes problems. Electronic Research Archive, 2021, 29 (1) : 1881-1895. doi: 10.3934/era.2020096 |
[5] |
Xufeng Xiao, Xinlong Feng, Jinyun Yuan. The stabilized semi-implicit finite element method for the surface Allen-Cahn equation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2857-2877. doi: 10.3934/dcdsb.2017154 |
[6] |
Jiaping Yu, Haibiao Zheng, Feng Shi, Ren Zhao. Two-grid finite element method for the stabilization of mixed Stokes-Darcy model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 387-402. doi: 10.3934/dcdsb.2018109 |
[7] |
Yinnian He, Yanping Lin, Weiwei Sun. Stabilized finite element method for the non-stationary Navier-Stokes problem. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 41-68. doi: 10.3934/dcdsb.2006.6.41 |
[8] |
Yueqiang Shang, Qihui Zhang. A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3119-3142. doi: 10.3934/dcdsb.2020222 |
[9] |
Derrick Jones, Xu Zhang. A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces. Electronic Research Archive, , () : -. doi: 10.3934/era.2021032 |
[10] |
Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 593-608. doi: 10.3934/dcdsb.2010.13.593 |
[11] |
Min Chen, Nghiem V. Nguyen, Shu-Ming Sun. Solitary-wave solutions to Boussinesq systems with large surface tension. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1153-1184. doi: 10.3934/dcds.2010.26.1153 |
[12] |
Samuel Walsh. Steady stratified periodic gravity waves with surface tension II: Global bifurcation. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3287-3315. doi: 10.3934/dcds.2014.34.3287 |
[13] |
Hyung Ju Hwang, Youngmin Oh, Marco Antonio Fontelos. The vanishing surface tension limit for the Hele-Shaw problem. Discrete & 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 & Continuous Dynamical Systems, 2014, 34 (8) : 3109-3123. doi: 10.3934/dcds.2014.34.3109 |
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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 |
[16] |
Nataliya Vasylyeva, Vitalii Overko. The Hele-Shaw problem with surface tension in the case of subdiffusion. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1941-1974. doi: 10.3934/cpaa.2016023 |
[17] |
Samuel Walsh. Steady stratified periodic gravity waves with surface tension I: Local bifurcation. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3241-3285. doi: 10.3934/dcds.2014.34.3241 |
[18] |
David J. Silvester, Alex Bespalov, Catherine E. Powell. A framework for the development of implicit solvers for incompressible flow problems. Discrete & Continuous Dynamical Systems - S, 2012, 5 (6) : 1195-1221. doi: 10.3934/dcdss.2012.5.1195 |
[19] |
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) : 3185-3213. doi: 10.3934/dcdsb.2015.20.3185 |
[20] |
Shengfu Deng. Generalized pitchfork bifurcation on a two-dimensional gaseous star with self-gravity and surface tension. Discrete & Continuous Dynamical Systems, 2014, 34 (9) : 3419-3435. doi: 10.3934/dcds.2014.34.3419 |
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