# American Institute of Mathematical Sciences

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

## A multi layer method applied to a model of phytoplankton

 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.
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 - A, 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] 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 [6] 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 [7] 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 [8] Carlos Cabrera, Peter Makienko, Peter Plaumann. Semigroup representations in holomorphic dynamics. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1333-1349. doi: 10.3934/dcds.2013.33.1333 [9] 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 [10] Yuchi Qiu, Weitao Chen, Qing Nie. A hybrid method for stiff reaction–diffusion equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-31. doi: 10.3934/dcdsb.2019144 [11] 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 [12] 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 [13] Xueyong Wang, Yiju Wang, Gang Wang. An accelerated augmented Lagrangian method for multi-criteria optimization problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-9. doi: 10.3934/jimo.2018136 [14] 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 [15] 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 [16] Xin Li, Xingfu Zou. On a reaction-diffusion model for sterile insect release method with release on the boundary. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2509-2522. doi: 10.3934/dcdsb.2012.17.2509 [17] Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reaction-diffusion patterns. Communications on Pure & Applied Analysis, 2012, 11 (1) : 189-207. doi: 10.3934/cpaa.2012.11.189 [18] Mi-Ho Giga, Yoshikazu Giga, Takeshi Ohtsuka, Noriaki Umeda. On behavior of signs for the heat equation and a diffusion method for data separation. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2277-2296. doi: 10.3934/cpaa.2013.12.2277 [19] Francisco Guillén-González, Mamadou Sy. Iterative method for mass diffusion model with density dependent viscosity. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 823-841. doi: 10.3934/dcdsb.2008.10.823 [20] Mihaela Negreanu, J. Ignacio Tello. On a comparison method to reaction-diffusion systems and its applications to chemotaxis. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2669-2688. doi: 10.3934/dcdsb.2013.18.2669

2018 Impact Factor: 0.871