Global existence of classical solutions to a chemotaxis-haptotaxis model

被引：1
作者：
Takhirov, Jozil [1 ]
机构：
[1] 81 Mirzo Ulugbek Str, Tashkent 100170, Uzbekistan
来源：
PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 2卷 / 01期
关键词：
Chemotaxis; Haptotaxis; Nonlinear diffusion; Boundedness; Global existence; COLLECTIVE CELL-MIGRATION; MATHEMATICAL-MODEL; CANCER INVASION; TUMOR INVASION; GROWTH; TISSUE; SYSTEM; PLASTICITY; DIFFUSION;
D O I：
10.1007/s42985-021-00069-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue. The model consists of three parabolic chemotaxis-haptotaxis PDEs describing interactions between cancer cells, matrix degrading enzymes and the host tissue. We prove the global existence and uniform boundedness in this competition system by some delicate a priori estimate techniques.
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页数：15
相关论文
共 47 条
  • [1] Alt W., 2003, Polymer and Cell Dynamics: Multiscale Modelling and Numerical Simulations, DOI [10.1007/978-3-0348-8043-5, DOI 10.1007/978-3-0348-8043-5]
  • [2] A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion
    Anderson, ARA
    [J]. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA, 2005, 22 (02): : 163 - 186
  • [3] [Anonymous], Report No. 19/2014,
  • [4] Cancer cell invasion and EMT marker expression: a three-dimensional study of the human cancer-host interface
    Bronsert, P.
    Enderle-Ammour, K.
    Bader, M.
    Timme, S.
    Kuehs, M.
    Csanadi, A.
    Kayser, G.
    Kohler, I.
    Bausch, D.
    Hoeppner, J.
    Hopt, U. T.
    Keck, T.
    Stickeler, E.
    Passlick, B.
    Schilling, O.
    Reiss, C. P.
    Vashist, Y.
    Brabletz, T.
    Berger, J.
    Lotz, J.
    Olesch, J.
    Werner, M.
    Wellner, U. F.
    [J]. JOURNAL OF PATHOLOGY, 2014, 234 (03) : 410 - 422
  • [5] Byrne H, 2003, MATH MED BIOL, V20, P341
  • [6] Chaplain MAJ, 2006, NETW HETEROG MEDIA, V1, P399
  • [7] Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development
    Chaplain, M. A. J.
    Graziano, L.
    Preziosi, L.
    [J]. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA, 2006, 23 (03): : 197 - 229
  • [8] Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system
    Chaplain, MAJ
    Lolas, G
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2005, 15 (11) : 1685 - 1734
  • [9] CHAPLAIN MAJ, 1993, J MATH BIOL, V31, P431, DOI 10.1007/BF00173886
  • [10] Dorman S., 2002, Silico Biol, V2, P1
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