On a Model for the Growth of an Invasive Avascular Tumor

被引：3
|
作者：
Avila, J. A. J. [1 ]
Lozada-Cruz, G. [2 ]
机构：
[1] Univ Fed Sao Joao del Rei, Dept Math & Stat, BR-36307904 Sao Joao Del Rei, MG, Brazil
[2] Univ Estadual Paulista, Dept Math, IBILCE, BR-15054000 Sao Paulo, Brazil
来源：
APPLIED MATHEMATICS & INFORMATION SCIENCES | 2013年 / 7卷 / 05期
关键词：
Invasive avascular tumor; traveling wave; existence of solution; numerical simulation;
D O I：
10.12785/amis/070524
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to study the 1D model of invasive avascular tumor growth, which takes into account cell division, death, and motility, proposed by Kolobov and collaborators in 2009. First, we examine the existence and uniqueness of the solution to this model. Second, we studied qualitatively and numerically the traveling wave solutions. Finally, we show some numerical simulations for the cell density and nutrient concentration.
引用
收藏
页码：1857 / 1863
页数：7
相关论文
共 50 条
  • [31] The effect of time delays on the dynamics of avascular tumor growth
    Byrne, HM
    MATHEMATICAL BIOSCIENCES, 1997, 144 (02) : 83 - 117
  • [32] COMPUTATIONAL MODELING OF SOLID TUMOR GROWTH: THE AVASCULAR STAGE
    Bresch, Didier
    Colin, Thierry
    Grenier, Emmanuel
    Ribba, Benjamin
    Saut, Olivier
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (04): : 2321 - 2344
  • [33] On the transversally isotropic pressure effect on avascular tumor growth
    Kariotou, Foteini
    Vafeas, Panayiotis
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (02) : 277 - 282
  • [34] Phase transition in tumor growth: I avascular development
    Izquierdo-Kulich, E.
    Rebelo, I.
    Tejera, E.
    Nieto-Villar, J. M.
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2013, 392 (24) : 6616 - 6623
  • [35] Cell-based models of avascular tumor growth
    Drasdo, D
    Dormann, S
    Hoehme, S
    Deutsch, A
    FUNCTION AND REGULATION OF CELLULAR SYSTEMS, 2004, : 367 - 378
  • [36] Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
    Scianna, Marco
    MATHEMATICAL BIOSCIENCES, 2024, 370
  • [37] A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment
    Fiandaca, Giada
    Bernardi, Sara
    Scianna, Marco
    Delitala, Marcello Edoardo
    JOURNAL OF THEORETICAL BIOLOGY, 2022, 535
  • [38] A mathematical model for the onset of avascular tumor growth in response to the loss of p53 function
    Levine, Howard
    Smiley, Michael
    Tucker, Anna
    Nilsen-Hamilton, Marit
    CANCER INFORMATICS, 2006, 2 : 163 - 188
  • [39] A new mathematical model for avascular tumour growth
    Sherratt, JA
    Chaplain, MAJ
    JOURNAL OF MATHEMATICAL BIOLOGY, 2001, 43 (04) : 291 - 312
  • [40] A new mathematical model for avascular tumour growth
    Jonathan A. Sherratt
    Mark A.J. Chaplain
    Journal of Mathematical Biology, 2001, 43 : 291 - 312
12345