May  2005, 5(2): 411-422. doi: 10.3934/dcdsb.2005.5.411

A mathematical evolution model for phytoremediation of metals

1. 

Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043, United States, United States

2. 

Department of Chemistry, New Jersey City University, Jersey City, NJ 07305, United States

Received  May 2003 Revised  May 2004 Published  February 2005

In the past few decades, efforts have been made to clean sites polluted by heavy metals such as chromium. One of the new innovative methods of eradicating metals from soil is phytoremediation. Phytoremediation uses plants to pull metals from the soil through the roots. This article develops a system of differential equations to model the plant metal interaction of phytoremediation. We prove there exists a threshold time, $t$*, where the amount of metals in the environment meet a prescribed EPA criteria. The cost of phytoremediating up to time $t$* is computed. The cost function can be used to estimate the feasibility of clearing a polluted site through phytoremediation as opposed to alternate techniques such as brown filling.
Citation: Diana M. Thomas, Lynn Vandemuelebroeke, Kenneth Yamaguchi. A mathematical evolution model for phytoremediation of metals. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 411-422. doi: 10.3934/dcdsb.2005.5.411
[1]

Ștefana-Lucia Aniţa. Optimal control for stochastic differential equations and related Kolmogorov equations. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2022023

[2]

Qi Lü, Xu Zhang. A concise introduction to control theory for stochastic partial differential equations. Mathematical Control and Related Fields, 2021  doi: 10.3934/mcrf.2021020

[3]

Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4099-4116. doi: 10.3934/dcdsb.2019052

[4]

Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control and Related Fields, 2018, 8 (3&4) : 809-828. doi: 10.3934/mcrf.2018036

[5]

Tatiana Filippova. Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty. Conference Publications, 2011, 2011 (Special) : 410-419. doi: 10.3934/proc.2011.2011.410

[6]

Yves Achdou, Mathieu Laurière. On the system of partial differential equations arising in mean field type control. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 3879-3900. doi: 10.3934/dcds.2015.35.3879

[7]

Wei Mao, Yanan Jiang, Liangjian Hu, Xuerong Mao. Stabilization by intermittent control for hybrid stochastic differential delay equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 569-581. doi: 10.3934/dcdsb.2021055

[8]

Guangjun Shen, Xueying Wu, Xiuwei Yin. Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 755-774. doi: 10.3934/dcdsb.2020133

[9]

Elena Goncharova, Maxim Staritsyn. On BV-extension of asymptotically constrained control-affine systems and complementarity problem for measure differential equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1061-1070. doi: 10.3934/dcdss.2018061

[10]

Frank Pörner, Daniel Wachsmuth. Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations. Mathematical Control and Related Fields, 2018, 8 (1) : 315-335. doi: 10.3934/mcrf.2018013

[11]

Jianhui Huang, Xun Li, Jiongmin Yong. A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon. Mathematical Control and Related Fields, 2015, 5 (1) : 97-139. doi: 10.3934/mcrf.2015.5.97

[12]

Ishak Alia. Time-inconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach. Mathematical Control and Related Fields, 2020, 10 (4) : 785-826. doi: 10.3934/mcrf.2020020

[13]

Yong Ren, Qi Zhang. Stabilization for hybrid stochastic differential equations driven by Lévy noise via periodically intermittent control. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3811-3829. doi: 10.3934/dcdsb.2021207

[14]

Robert J. Kipka, Yuri S. Ledyaev. Optimal control of differential inclusions on manifolds. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4455-4475. doi: 10.3934/dcds.2015.35.4455

[15]

Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 209-226. doi: 10.3934/dcdsb.2017011

[16]

Wensheng Yin, Jinde Cao, Guoqiang Zheng. Further results on stabilization of stochastic differential equations with delayed feedback control under $ G $-expectation framework. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 883-901. doi: 10.3934/dcdsb.2021072

[17]

Miriam Manoel, Patrícia Tempesta. Binary differential equations with symmetries. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1957-1974. doi: 10.3934/dcds.2019082

[18]

Elimhan N. Mahmudov. Optimal control of evolution differential inclusions with polynomial linear differential operators. Evolution Equations and Control Theory, 2019, 8 (3) : 603-619. doi: 10.3934/eect.2019028

[19]

Nidhal Gammoudi, Hasnaa Zidani. A differential game control problem with state constraints. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022008

[20]

Guillaume Bal, Alexandre Jollivet. Boundary control for transport equations. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022014

2021 Impact Factor: 1.497

Metrics

  • PDF downloads (259)
  • HTML views (0)
  • Cited by (26)

[Back to Top]