Partial-moment minimum-entropy models for kinetic chemotaxis equations in one and two dimensions

被引：4
作者：
Ritter, Juliane [1 ]
Klar, Axel [1 ]
Schneider, Florian [1 ]
机构：
[1] TU Kaiserslautern, Fachbereich Math, Erwin Schrodinger Str, D-67663 Kaiserslautern, Germany
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 306卷
关键词：
Chemotaxis; Moment models; Minimum entropy; RADIATIVE HEAT-TRANSFER; FOKKER-PLANCK EQUATION; KELLER-SEGEL MODEL; BLOW-UP; DIFFUSION; FLUX; APPROXIMATIONS; AGGREGATION; INSTABILITY; TRANSPORT;
D O I：
10.1016/j.cam.2016.04.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic equation for the cell densities we apply a half-/quarter-moments method with different closure relations to derive macroscopic equations. Appropriate numerical schemes are presented as well as numerical results for several test cases. The resulting solutions are compared to kinetic reference solutions and solutions computed using a full moment method with a linear superposition strategy. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：300 / 315
页数：16
相关论文
共 38 条
  • [1] ALT W, 1980, LECT NOTES BIOMATH, V38, P353
  • [2] [Anonymous], 2015, VERSION 850197613 R2
  • [3] Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues
    Bellomo, N.
    Bellouquid, A.
    Tao, Y.
    Winkler, M.
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2015, 25 (09) : 1663 - 1763
  • [4] ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES
    Bellomo, N.
    Bellouquid, A.
    Nieto, J.
    Soler, J.
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2012, 22 (01)
  • [5] MODELING CHEMOTAXIS FROM L2-CLOSURE MOMENTS IN KINETIC THEORY OF ACTIVE PARTICLES
    Bellomo, Nicola
    Bellouquid, Abdelghani
    Nieto, Juanjo
    Soler, Juan
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (04): : 847 - 863
  • [6] MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS
    Bellomo, Nicola
    Bellouquid, Abdelghani
    Nieto, Juan
    Soler, Juan
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2010, 20 (07) : 1179 - 1207
  • [7] The one-dimensional Keller-Segel model with fractional diffusion of cells
    Bournaveas, Nikolaos
    Calvez, Vincent
    [J]. NONLINEARITY, 2010, 23 (04) : 923 - 935
  • [8] Volume effects in the Keller-Segel model: energy estimates preventing blow-up
    Calvez, Vincent
    Carrillo, Jose A.
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2006, 86 (02): : 155 - 175
  • [9] Kinetic models for chemotaxis and their drift-diffusion limits
    Chalub, FACC
    Markowich, PA
    Perthame, B
    Schmeiser, C
    [J]. MONATSHEFTE FUR MATHEMATIK, 2004, 142 (1-2): : 123 - 141
  • [10] Jeans type instability for a chemotactic model of cellular aggregation
    Chavanis, P. H.
    [J]. EUROPEAN PHYSICAL JOURNAL B, 2006, 52 (03) : 433 - 443
1234