Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 3
Submit an article Journal homepage
102
Views
2
CrossRef citations to date
0
Altmetric
Research Article

A free boundary problem for necrotic tumor growth with angiogenesis

Shihe Xua School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, People's Republic of ChinaCorrespondence[email protected] [email protected]
View further author information
,
Fangwei Zhangb School of Navigation and Shipping, Shandong Jiaotong University, Weihai, People's Republic of ChinaView further author information
&
Qinghua Zhouc School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, People's Republic of ChinaView further author information
Pages 977-987 | Received 12 Mar 2020, Accepted 10 Aug 2021, Published online: 20 Aug 2021

References

  • Byrne H. The effect of time delays on the dynamics of avascular tumor growth. Math Biosci. 1997;144:83–117.
  • Byrne H, Chaplain M. Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math Biosci. 1995;130:151–181.
  • Byrne H, Chaplain M. Growth of necrotic tumors in the presence and absence of inhibitors. Math Biosci. 1996;135:187–216.
  • Greenspan H. Models for the growth of solid tumor by diffusion. Stud Appl Math. 1972;51:317–340.
  • Greenspan H. On the growth and stability of cell cultures and solid tumors. J Theor Biol. 1976;56:229–242.
  • Piotrowska MJ. Hopf bifurcation in a solid asascular tumor growth model with two discrete delays. Math Comput Model. 2008;47:597–603.
  • Thompson K, Byrne H. Modelling the internalisation of labelled cells in tumor spheroids. Bull Math Biol. 1999;61:601–623.
  • Ward J, King J. Mathematical modelling of avascular-tumor growth II: modelling growth saturation. IMA J Math Appl Med Biol. 1998;15:1–42.
  • Wu J, Zhou F. Asymptotic behavior of solutions of a free boundary problem modeling tumor spheroid with Gibbs–Thomson relation. J Differ Equ. 2017;262:4907–4930.
  • Xu S, Bai M, Zhang FW. Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients. J Biol Dynam. 2017;11:504–520.
  • Cui S. Analysis of a free boundary problem modeling tumor growth. Acta Math Sinica. 2005;21:1071–1082.
  • Cui S. Formation of necrotic cores in the griwth of tumors: analytic results. Acta Math Scientia. 2006;26B:781–796.
  • Cui S, Xu S. Analysis of mathematical models for the growth of tumors with time delays in cell proliferation. J Math Anal Appl. 2007;336:523–541.
  • Friedman A, Reitich F. Analysis of a mathematical model for the growth of tumors. J Math Biol. 1999;38:262–284.
  • Fu S, Cui S. Global existence and stability of solution of a reaction-diffusion model for cancer invasion. Nonlinear Anal Real World Appl. 2009;10:1362–1369.
  • Shen H, Wei X. A qualitative analysis of a free boundary problem modeling tumor growth with angiogenesis. Nonlinear Anal Real World Appl. 2019;47:106–126.
  • Bodnar M, Foryś U. Time delay in necrotic core formation. Math Biosci Eng. 2005;2:461–472.
  • Cui S. Analysis of a mathematical model for the growth of tumors under the action of external inhibitors. J Math Biol. 2002;44:395–426.
  • Foryś U, Mokwa-Borkowska A. Solid tumour growth analysis of necrotic core formation. Math Comput Model. 2005;42:593–600.
  • Wu J, Wang C. Radially symmetric growth of necrotic tumors and connection with nonnecrotic tumors. Nonlinear Anal Real World Appl. 2019;50:25–33.
  • Friedman A, Lam K. Analysis of a free-boundary tumor model with angiogenesis. J Differ Equ. 2015;259:7636–7661.
  • Zhuang Y, Cui S. Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis. J Differ Equa. 2018;265:620–644.
  • Xu S, Su D. Analysis of necrotic core formation in angiogenic tumor growth. Nonlinear Anal Real World Appl. 2020;51:12.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.