American Institute of Mathematical Sciences

Advanced
September  2004, 3(3): 331-352. doi: 10.3934/cpaa.2004.3.331

The evolution of a tumor cord cell population

Janet Dyson 1, , Rosanna Villella-Bressan 2, and  G. F. Webb 3,

1. 

Department of Mathematics, Mansfield College, Oxford University, Oxford, England
2. 

Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padua
3. 

Department of Mathematics, Vanderbilt University, Nashville, TN 37235, United States

Received  March 2003 Revised  February 2004 Published  June 2004

A model of a tumor cord cell population is analyzed in which individual cells are distinguished by cell age and radial position. The existence and asymptotic behavior of solutions are investigated. It is proved that solutions are asymptotically eventually periodic.
Keywords: nonlinear rst order partial di erential equation, asymptotic behavior., Tumor cord cell population.
Mathematics Subject Classification: Primary 34l60, 92D25, 92C5.
Citation: Janet Dyson, Rosanna Villella-Bressan, G. F. Webb. The evolution of a tumor cord cell population. Communications on Pure & Applied Analysis, 2004, 3 (3) : 331-352. doi: 10.3934/cpaa.2004.3.331
[1]

Janet Dyson, Rosanna Villella-Bressan, G.F. Webb. The steady state of a maturity structured tumor cord cell population. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 115-134. doi: 10.3934/dcdsb.2004.4.115
[2]

Junde Wu, Shihe Xu. Asymptotic behavior of a nonlinear necrotic tumor model with a periodic external nutrient supply. Discrete & Continuous Dynamical Systems - B, 2020, 25 (7) : 2453-2460. doi: 10.3934/dcdsb.2020018
[3]

Mostafa Adimy, Laurent Pujo-Menjouet. Asymptotic behavior of a singular transport equation modelling cell division. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 439-456. doi: 10.3934/dcdsb.2003.3.439
[4]

Jean-Claude Saut, Jun-Ichi Segata. Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 219-239. doi: 10.3934/dcds.2019009
[5]

Genni Fragnelli, A. Idrissi, L. Maniar. The asymptotic behavior of a population equation with diffusion and delayed birth process. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 735-754. doi: 10.3934/dcdsb.2007.7.735
[6]

Yongqin Liu. Asymptotic behavior of solutions to a nonlinear plate equation with memory. Communications on Pure & Applied Analysis, 2017, 16 (2) : 533-556. doi: 10.3934/cpaa.2017027
[7]

Raegan Higgins. Asymptotic behavior of second-order nonlinear dynamic equations on time scales. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 609-622. doi: 10.3934/dcdsb.2010.13.609
[8]

Hongwei Zhang, Qingying Hu. Asymptotic behavior and nonexistence of wave equation with nonlinear boundary condition. Communications on Pure & Applied Analysis, 2005, 4 (4) : 861-869. doi: 10.3934/cpaa.2005.4.861
[9]

Thierry Cazenave, Zheng Han. Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation. Discrete & Continuous Dynamical Systems, 2020, 40 (8) : 4801-4819. doi: 10.3934/dcds.2020202
[10]

Nakao Hayashi, Pavel I. Naumkin. Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited. Discrete & Continuous Dynamical Systems, 1997, 3 (3) : 383-400. doi: 10.3934/dcds.1997.3.383
[11]

Z. Jackiewicz, B. Zubik-Kowal, B. Basse. Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics. Mathematical Biosciences & Engineering, 2009, 6 (3) : 561-572. doi: 10.3934/mbe.2009.6.561
[12]

Mamoru Okamoto. Asymptotic behavior of solutions to a higher-order KdV-type equation with critical nonlinearity. Evolution Equations & Control Theory, 2019, 8 (3) : 567-601. doi: 10.3934/eect.2019027
[13]

Luca Calatroni, Bertram Düring, Carola-Bibiane Schönlieb. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. Discrete & Continuous Dynamical Systems, 2014, 34 (3) : 931-957. doi: 10.3934/dcds.2014.34.931
[14]

Keng Deng, Yixiang Wu. Asymptotic behavior for a reaction-diffusion population model with delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 385-395. doi: 10.3934/dcdsb.2015.20.385
[15]

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
[16]

Cecilia Cavaterra, Maurizio Grasselli. Asymptotic behavior of population dynamics models with nonlocal distributed delays. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 861-883. doi: 10.3934/dcds.2008.22.861
[17]

Chunqing Lu. Asymptotic solutions of a nonlinear equation. Conference Publications, 2003, 2003 (Special) : 590-595. doi: 10.3934/proc.2003.2003.590
[18]

Lie Zheng. Asymptotic behavior of solutions to the nonlinear breakage equations. Communications on Pure & Applied Analysis, 2005, 4 (2) : 463-473. doi: 10.3934/cpaa.2005.4.463
[19]

Irena Lasiecka, W. Heyman. Asymptotic behavior of solutions in nonlinear dynamic elasticity. Discrete & Continuous Dynamical Systems, 1995, 1 (2) : 237-252. doi: 10.3934/dcds.1995.1.237
[20]

Georges Chamoun, Moustafa Ibrahim, Mazen Saad, Raafat Talhouk. Asymptotic behavior of solutions of a nonlinear degenerate chemotaxis model. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4165-4188. doi: 10.3934/dcdsb.2020092

2020 Impact Factor: 1.916

Tools

Metrics

  • PDF downloads (39)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences