IDEAS home Printed from https://ideas.repec.org/a/hin/complx/9683982.html
   My bibliography  Save this article

Analysis of a Delayed Free Boundary Problem with Application to a Model for Tumor Growth of Angiogenesis

Author

Listed:
  • Shihe Xu
  • Fangwei Zhang

Abstract

In this paper, we consider a time-delayed free boundary problem with time dependent Robin boundary conditions. The special case where is a mathematical model for the growth of a solid nonnecrotic tumor with angiogenesis. In the problem, both the angiogenesis and the time delay are taken into consideration. Tumor cell division takes a certain length of time, thus we assume that the proliferation process leg behind as compared to the process of apoptosis. The angiogenesis is reflected as the time dependent Robin boundary condition in the model. Global existence and uniqueness of the nonnegative solution of the problem is proved. When is sufficiently small, the stability of the steady state solution is studied, where is the ratio of the time scale of diffusion to the tumor doubling time scale. Under some conditions, the results show that the magnitude of the delay does not affect the final dynamic behavior of the solutions. An application of our results to a mathematical model for tumor growth of angiogenesis is given and some numerical simulations are also given.

Suggested Citation

  • Shihe Xu & Fangwei Zhang, 2020. "Analysis of a Delayed Free Boundary Problem with Application to a Model for Tumor Growth of Angiogenesis," Complexity, Hindawi, vol. 2020, pages 1-12, February.
    • Handle: RePEc:hin:complx:9683982
    DOI: 10.1155/2020/9683982
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2020/9683982.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2020/9683982.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/9683982?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhou, Haihua & Wang, Zejia & Yuan, Daming & Song, Huijuan, 2021. "Hopf bifurcation of a free boundary problem modeling tumor growth with angiogenesis and two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:9683982. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.