American Institute of Mathematical Sciences

Advanced
March  2007, 2(1): 37-54. doi: 10.3934/nhm.2007.2.37

A multi layer method applied to a model of phytoplankton

Khalid Boushaba 1,

1. 

Iowa State University, Department of Mathematics, 482 Carver Hall Ames, IA 50011

Received  July 2006 Revised  December 2006 Published  December 2006

In this paper, we develop a multi layer method to solve a generalized case of a phytoplankton model introduced in [7]. It is treated by means of a sequence of approximations: the mixed layer is subdivided into a finite number of thin layers within each of which horizontal velocity can be considered constant with respect to depth. Existence, uniqueness and non negativity of solutions are investigated.
Keywords: multi layer method, method of lines, vertical diffusion, semigroup, sea current, Phytoplankton dynamics.
Mathematics Subject Classification: Primary: 47D06, 65M20,65M25, 74G55, 34K1.
Citation: Khalid Boushaba. A multi layer method applied to a model of phytoplankton. Networks & Heterogeneous Media, 2007, 2 (1) : 37-54. doi: 10.3934/nhm.2007.2.37
[1]

Masahiro Yamaguchi, Yasuhiro Takeuchi, Wanbiao Ma. Population dynamics of sea bass and young sea bass. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 833-840. doi: 10.3934/dcdsb.2004.4.833
[2]

Stanisław Migórski, Shengda Zeng. The Rothe method for multi-term time fractional integral diffusion equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 719-735. doi: 10.3934/dcdsb.2018204
[3]

Xin Yu, Guojie Zheng, Chao Xu. The $C$-regularized semigroup method for partial differential equations with delays. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 5163-5181. doi: 10.3934/dcds.2016024
[4]

N. Romero, A. Rovella, F. Vilamajó. Dynamics of vertical delay endomorphisms. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 409-422. doi: 10.3934/dcdsb.2003.3.409
[5]

Jie Zhang, Shuang Lin, Li-Wei Zhang. A log-exponential regularization method for a mathematical program with general vertical complementarity constraints. Journal of Industrial & Management Optimization, 2013, 9 (3) : 561-577. doi: 10.3934/jimo.2013.9.561
[6]

Liping Pang, Na Xu, Jian Lv. The inexact log-exponential regularization method for mathematical programs with vertical complementarity constraints. Journal of Industrial & Management Optimization, 2019, 15 (1) : 59-79. doi: 10.3934/jimo.2018032
[7]

Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines. Inverse Problems & Imaging, 2013, 7 (2) : 307-340. doi: 10.3934/ipi.2013.7.307
[8]

Behzad Ghanbari, Devendra Kumar, Jagdev Singh. An efficient numerical method for fractional model of allelopathic stimulatory phytoplankton species with Mittag-Leffler law. Discrete & Continuous Dynamical Systems - S, 2021, 14 (10) : 3577-3587. doi: 10.3934/dcdss.2020428
[9]

Carlos Cabrera, Peter Makienko, Peter Plaumann. Semigroup representations in holomorphic dynamics. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1333-1349. doi: 10.3934/dcds.2013.33.1333
[10]

Zhiming Chen, Chao Liang, Xueshuang Xiang. An anisotropic perfectly matched layer method for Helmholtz scattering problems with discontinuous wave number. Inverse Problems & Imaging, 2013, 7 (3) : 663-678. doi: 10.3934/ipi.2013.7.663
[11]

Yuchi Qiu, Weitao Chen, Qing Nie. A hybrid method for stiff reaction–diffusion equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6387-6417. doi: 10.3934/dcdsb.2019144
[12]

Martin Burger, José A. Carrillo, Marie-Therese Wolfram. A mixed finite element method for nonlinear diffusion equations. Kinetic & Related Models, 2010, 3 (1) : 59-83. doi: 10.3934/krm.2010.3.59
[13]

Xiaoling Sun, Xiaojin Zheng, Juan Sun. A Lagrangian dual and surrogate method for multi-dimensional quadratic knapsack problems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 47-60. doi: 10.3934/jimo.2009.5.47
[14]

Xueyong Wang, Yiju Wang, Gang Wang. An accelerated augmented Lagrangian method for multi-criteria optimization problem. Journal of Industrial & Management Optimization, 2020, 16 (1) : 1-9. doi: 10.3934/jimo.2018136
[15]

Foxiang Liu, Lingling Xu, Yuehong Sun, Deren Han. A proximal alternating direction method for multi-block coupled convex optimization. Journal of Industrial & Management Optimization, 2019, 15 (2) : 723-737. doi: 10.3934/jimo.2018067
[16]

Li Deng, Wenjie Bi, Haiying Liu, Kok Lay Teo. A multi-stage method for joint pricing and inventory model with promotion constrains. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1653-1682. doi: 10.3934/dcdss.2020097
[17]

Zhenwei Zhang, Xue Li, Yuping Duan, Ke Yin, Xue-Cheng Tai. An efficient multi-grid method for TV minimization problems. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021034
[18]

Yuan-mei Xia, Xin-min Yang, Ke-quan Zhao. A combined scalarization method for multi-objective optimization problems. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2669-2683. doi: 10.3934/jimo.2020088
[19]

Jean-Jacques Kengwoung-Keumo. Dynamics of two phytoplankton populations under predation. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1319-1336. doi: 10.3934/mbe.2014.11.1319
[20]

Daniele Andreucci, Dario Bellaveglia, Emilio N.M. Cirillo, Silvia Marconi. Effect of intracellular diffusion on current--voltage curves in potassium channels. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1837-1853. doi: 10.3934/dcdsb.2014.19.1837

2020 Impact Factor: 1.213

Tools

Metrics

  • PDF downloads (32)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences