American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 1-12. doi: 10.3934/proc.2011.2011.1

Difference approximation for an amphibian juvenile-adult dispersal mode

Azmy S. Ackleh 1, , Keng Deng 1, and  Qihua Huang 2,

1. 

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010, United States
2. 

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States

Received  July 2010 Revised  April 2011 Published  September 2011

We consider an amphibian juvenile-adult population dispersing between ponds. We assume that juveniles (tadpoles) are structured by age and adults (frogs) are structured by size. This leads to a system of first order nonlocal hyperbolic equations. A finite difference approximation to this system is developed. Existence-uniqueness of the weak solution to the system is established and convergence of the finite difference approximation to the unique solution is proved.
Keywords: existence-uniqueness., implicit finite difference approximation, Juvenile-adult dispersal model.
Mathematics Subject Classification: 35L50, 65M06, 92D25.
Citation: Azmy S. Ackleh, Keng Deng, Qihua Huang. Difference approximation for an amphibian juvenile-adult dispersal mode. Conference Publications, 2011, 2011 (Special) : 1-12. doi: 10.3934/proc.2011.2011.1
[1]

J. M. Cushing, Simon Maccracken Stump. Darwinian dynamics of a juvenile-adult model. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1017-1044. doi: 10.3934/mbe.2013.10.1017
[2]

Azmy S. Ackleh, Keng Deng. Stability of a delay equation arising from a juvenile-adult model. Mathematical Biosciences & Engineering, 2010, 7 (4) : 729-737. doi: 10.3934/mbe.2010.7.729
[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]

József Z. Farkas, Thomas Hagen. Asymptotic behavior of size-structured populations via juvenile-adult interaction. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 249-266. doi: 10.3934/dcdsb.2008.9.249
[5]

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
[6]

Mou-Hsiung Chang, Tao Pang, Moustapha Pemy. Finite difference approximation for stochastic optimal stopping problems with delays. Journal of Industrial & Management Optimization, 2008, 4 (2) : 227-246. doi: 10.3934/jimo.2008.4.227
[7]

Giovanna Citti, Maria Manfredini, Alessandro Sarti. Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space. Communications on Pure & Applied Analysis, 2010, 9 (4) : 905-927. doi: 10.3934/cpaa.2010.9.905
[8]

Pavlos Xanthopoulos, Georgios E. Zouraris. A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 239-263. doi: 10.3934/dcdsb.2008.10.239
[9]

Gonzalo Galiano, Julián Velasco. Finite element approximation of a population spatial adaptation model. Mathematical Biosciences & Engineering, 2013, 10 (3) : 637-647. doi: 10.3934/mbe.2013.10.637
[10]

Xin Lai, Xinfu Chen, Mingxin Wang, Cong Qin, Yajing Zhang. Existence, uniqueness, and stability of bubble solutions of a chemotaxis model. Discrete & Continuous Dynamical Systems, 2016, 36 (2) : 805-832. doi: 10.3934/dcds.2016.36.805
[11]

Ahmed Aghriche, Radouane Yafia, M. A. Aziz Alaoui, Abdessamad Tridane. Oscillations induced by quiescent adult female in a model of wild aedes aegypti mosquitoes. Discrete & Continuous Dynamical Systems - S, 2020, 13 (9) : 2443-2463. doi: 10.3934/dcdss.2020194
[12]

Inger Daniels, Catherine Lebiedzik. Existence and uniqueness of a structural acoustic model involving a nonlinear shell. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 243-252. doi: 10.3934/dcdss.2008.1.243
[13]

Stefanie Hirsch, Dietmar Ölz, Christian Schmeiser. Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 4945-4962. doi: 10.3934/dcds.2016014
[14]

T. Tachim Medjo. On the existence and uniqueness of solution to a stochastic simplified liquid crystal model. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2243-2264. doi: 10.3934/cpaa.2019101
[15]

Hiroshi Matano, Yoichiro Mori. Global existence and uniqueness of a three-dimensional model of cellular electrophysiology. Discrete & Continuous Dynamical Systems, 2011, 29 (4) : 1573-1636. doi: 10.3934/dcds.2011.29.1573
[16]

Telma Silva, Adélia Sequeira, Rafael F. Santos, Jorge Tiago. Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 343-362. doi: 10.3934/dcdss.2016.9.343
[17]

Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707
[18]

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
[19]

Claire david@lmm.jussieu.fr David, Pierre Sagaut. Theoretical optimization of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 286-293. doi: 10.3934/proc.2007.2007.286
[20]

Guillermo Reyes, Juan-Luis Vázquez. The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1275-1294. doi: 10.3934/cpaa.2008.7.1275

 Impact Factor: 

Tools

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences