2009, 11(3): 563-585. doi: 10.3934/dcdsb.2009.11.563

Coagulation, fragmentation and growth processes in a size structured population

1. 

School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa

2. 

Department of Mathematics, Strathclyde University, Glasgow, Scotland, United Kingdom

Received  January 2008 Revised  July 2008 Published  March 2009

An equation describing the dynamical behaviour of phytoplankton cells is considered in which the effects of cell division and aggregration are incorporated by coupling the coagulation-fragmentation equation with the McKendrick-von Foerster renewal model of an age-structured population. Under appropriate conditions on the model parameters, the associated initial-boundary value problem is shown to be well posed in a physically relevant Banach space.
Citation: Jacek Banasiak, Wilson Lamb. Coagulation, fragmentation and growth processes in a size structured population. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 563-585. doi: 10.3934/dcdsb.2009.11.563
[1]

L. M. Abia, O. Angulo, J.C. López-Marcos. Size-structured population dynamics models and their numerical solutions. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1203-1222. doi: 10.3934/dcdsb.2004.4.1203

[2]

Dongxue Yan, Xianlong Fu. Asymptotic behavior of a hierarchical size-structured population model. Evolution Equations & Control Theory, 2018, 7 (2) : 293-316. doi: 10.3934/eect.2018015

[3]

Xianlong Fu, Dongmei Zhu. Stability analysis for a size-structured juvenile-adult population model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 391-417. doi: 10.3934/dcdsb.2014.19.391

[4]

Xianlong Fu, Dongmei Zhu. Stability results for a size-structured population model with delayed birth process. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 109-131. doi: 10.3934/dcdsb.2013.18.109

[5]

Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041

[6]

Rinaldo M. Colombo, Mauro Garavello. Stability and optimization in structured population models on graphs. Mathematical Biosciences & Engineering, 2015, 12 (2) : 311-335. doi: 10.3934/mbe.2015.12.311

[7]

Jianquan Li, Zhien Ma. Stability analysis for SIS epidemic models with vaccination and constant population size. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 635-642. doi: 10.3934/dcdsb.2004.4.635

[8]

Pierre Degond, Maximilian Engel. Numerical approximation of a coagulation-fragmentation model for animal group size statistics. Networks & Heterogeneous Media, 2017, 12 (2) : 217-243. doi: 10.3934/nhm.2017009

[9]

Wilson Lamb, Adam McBride, Louise Smith. Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5177-5187. doi: 10.3934/dcds.2013.33.5177

[10]

Bruno Buonomo, Deborah Lacitignola. On the stabilizing effect of cannibalism in stage-structured population models. Mathematical Biosciences & Engineering, 2006, 3 (4) : 717-731. doi: 10.3934/mbe.2006.3.717

[11]

Inom Mirzaev, David M. Bortz. A numerical framework for computing steady states of structured population models and their stability. Mathematical Biosciences & Engineering, 2017, 14 (4) : 933-952. doi: 10.3934/mbe.2017049

[12]

Hal L. Smith, Horst R. Thieme. Persistence and global stability for a class of discrete time structured population models. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4627-4646. doi: 10.3934/dcds.2013.33.4627

[13]

Dongxue Yan, Xianlong Fu. Asymptotic analysis of a spatially and size-structured population model with delayed birth process. Communications on Pure & Applied Analysis, 2016, 15 (2) : 637-655. doi: 10.3934/cpaa.2016.15.637

[14]

Qihua Huang, Hao Wang. A toxin-mediated size-structured population model: Finite difference approximation and well-posedness. Mathematical Biosciences & Engineering, 2016, 13 (4) : 697-722. doi: 10.3934/mbe.2016015

[15]

Dongxue Yan, Yu Cao, Xianlong Fu. Asymptotic analysis of a size-structured cannibalism population model with delayed birth process. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1975-1998. doi: 10.3934/dcdsb.2016032

[16]

Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 233-258. doi: 10.3934/mbe.2015.12.233

[17]

Jon Jacobsen, Taylor McAdam. A boundary value problem for integrodifference population models with cyclic kernels. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3191-3207. doi: 10.3934/dcdsb.2014.19.3191

[18]

Song Liang, Yuan Lou. On the dependence of population size upon random dispersal rate. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2771-2788. doi: 10.3934/dcdsb.2012.17.2771

[19]

Yingli Pan, Ying Su, Junjie Wei. Bistable waves of a recursive system arising from seasonal age-structured population models. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 511-528. doi: 10.3934/dcdsb.2018184

[20]

Ankik Kumar Giri. On the uniqueness for coagulation and multiple fragmentation equation. Kinetic & Related Models, 2013, 6 (3) : 589-599. doi: 10.3934/krm.2013.6.589

2017 Impact Factor: 0.972

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]