Finite volume methods for degenerate chemotaxis model

被引：30
|
作者：
Andreianov, Boris [2 ]
Bendahmane, Mostafa [1 ]
Saad, Mazen [3 ]
机构：
[1] Univ Bordeaux 2, Inst Math Bordeaux, F-33076 Bordeaux, France
[2] Univ Franche Comte, CNRS, UMR 6623, Math Lab, F-25030 Besancon, France
[3] CNRS, UMR 6629, Lab Math Jean Leray, Ecole Cent Nantes,Dept Informat & Math, F-44321 Nantes 3, France
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 14期
关键词：
Degenerate; Reaction-diffusion; Chemotaxis; Finite volume scheme; KELLER-SEGEL MODEL; NONLINEAR DIFFUSION; PARABOLIC EQUATIONS; PREVENTION; SCHEME;
D O I：
10.1016/j.cam.2011.02.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A finite volume method for solving the degenerate chemotaxis model is presented, along with numerical examples. This model consists of a degenerate parabolic convection-diffusion PDE for the density of the cell-population coupled to a parabolic PDE for the chemoattractant concentration. It is shown that discrete solutions exist, and the scheme converges. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码：4015 / 4031
页数：17
相关论文
共 50 条
  • [41] FINITE TRAVELING WAVE SOLUTIONS IN A DEGENERATE CROSS-DIFFUSION MODEL FOR BACTERIAL COLONY WITH VOLUME FILLING
    Bao, Lianzhang
    Gao, Wenjie
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (07): : 2813 - 2829
  • [42] Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model
    Cances, Clement
    Nabet, Flore
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2021, 55 (03): : 969 - 1003
  • [43] Finite-volume scheme for a degenerate cross-diffusion model motivated from ion transport
    Cances, Clement
    Chainais-Hillairet, Claire
    Gerstenmayer, Anita
    Juengel, Ansgar
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (02) : 545 - 575
  • [44] An Analysis on the Finite Volume Schemes and the Discrete Lyapunov Inequalities for the Chemotaxis System
    Guanyu Zhou
    Journal of Scientific Computing, 2021, 87
  • [45] An Analysis on the Finite Volume Schemes and the Discrete Lyapunov Inequalities for the Chemotaxis System
    Zhou, Guanyu
    JOURNAL OF SCIENTIFIC COMPUTING, 2021, 87 (02)
  • [46] Mixed finite element-finite volume methods
    Zine Dine, Khadija
    Achtaich, Naceur
    Chagdali, Mohamed
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2010, 17 (03) : 385 - 410
  • [47] COMPARISON OF FINITE VOLUME AND FINITE DIFFERENCE METHODS AND APPLICATION
    Faure, S.
    Pham, D.
    Temam, R.
    ANALYSIS AND APPLICATIONS, 2006, 4 (02) : 163 - 208
  • [48] A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS
    Droniou, Jerome
    Eymard, Robert
    Gallouet, Thierry
    Herbin, Raphaele
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2010, 20 (02): : 265 - 295
  • [49] Traveling Wavefronts in a Volume-Filling Chemotaxis Model
    Ou, Chunhua
    Yuan, Wei
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2009, 8 (01): : 390 - 416
  • [50] Fractional step methods applied to a chemotaxis model
    Rebecca Tyson
    L.G. Stern
    Randall J. LeVeque
    Journal of Mathematical Biology, 2000, 41 : 455 - 475
12345