Qualitative analysis of necrotic hyperbolic tumor growth model with Robin free boundary

HU Die; WEI Xuemei; FENG Zhaoyong; LIU Chengxia

doi:10.13471/j.cnki.acta.snus.2021A006

您当前的位置：

首页 >

文章列表页 >

Qualitative analysis of necrotic hyperbolic tumor growth model with Robin free boundary

Research articles | 更新时间：2023-11-01

- Qualitative analysis of necrotic hyperbolic tumor growth model with Robin free boundary
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 60, Issue 6, Pages: 150-160(2021)
- 作者机构：
  
  1.广东工业大学数学与统计学院，广东广州 510520
  2.中山大学数学学院，广东广州 510275
  3.南方医科大学口腔医院，广东广州 510280
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2021A006
  CLC： O175
- Published：25 November 2021，
  
  Published Online：27 September 2021，
  
  Received：16 January 2021，
  
  Accepted：24 April 2021
扫描看全文
胡蝶,卫雪梅,冯兆永等.具有Robin自由边界的坏死核双曲型肿瘤生长模型的定性分析[J].中山大学学报(自然科学版),2021,60(06):150-160.

HU Die,WEI Xuemei,FENG Zhaoyong,et al.Qualitative analysis of necrotic hyperbolic tumor growth model with Robin free boundary[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(06):150-160.
胡蝶,卫雪梅,冯兆永等.具有Robin自由边界的坏死核双曲型肿瘤生长模型的定性分析[J].中山大学学报(自然科学版),2021,60(06):150-160. DOI： 10.13471/j.cnki.acta.snus.2021A006.

HU Die,WEI Xuemei,FENG Zhaoyong,et al.Qualitative analysis of necrotic hyperbolic tumor growth model with Robin free boundary[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(06):150-160. DOI： 10.13471/j.cnki.acta.snus.2021A006.

摘要

研究了一个具有坏死核的双曲型肿瘤生长的Robin自由边界问题。该模型包含了一个描述营养物浓度变化的椭圆型方程，一个描述肿瘤半径的常微分方程和三个分别描述增殖细胞，休眠细胞和死亡细胞演化的一阶非线性双曲偏微分方程。通过特征线方法和

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507435&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507444&type=

9.31333351

2.28600001

不动点定理证明了该模型整体解的存在唯一性。同时证明了当

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507452&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507447&type=

8.89000034

3.21733332

时，

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507473&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507456&type=

20.15066719

4.06400013

Abstract

The necrotic hyperbolic tumor growth model with Robin free boundary is studied.The model contains an elliptic equation describing the diffusion of nutrient in the tumor，an ordinary differential equation describing tumor radius，and three nonlinear first-order hyperbolic partial differential equations describing the evolution of proliferating cells，quiescent cells and dead cells，respectively.By applying the characteristic theory of hyperbolic equations and the Banach fixed point theorem，the existence and uniqueness of the global solution of the model are proved.It is proven that

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507465&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507461&type=

23.19866753

4.57200003

in the case

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507487&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507467&type=

11.51466751

3.80999994

关键词

肿瘤生长坏死核自由边界问题整体解

Keywords

tumor growthnecrotic corefree boundary problemglobal solution

references

BYRNE H M， CHAPLAIN M A J. Growth of nonnecrotic tumors in the presence and absence of inhibitors ［J］. Mathematical Biosciences， 1995， 130（2）： 151-181.

BYRNE H M， CHAPLAIN M A J. Growth of necrotic tumors in the presence and absence of inhibitors ［J］. Mathematical Biosciences， 1996， 135（2）： 187-216.

崔尚斌. 肿瘤生长的自由边界问题［J］. 数学进展， 2009， 38（1）： 1-18.

FRIEDMAN A， REITICH F. Analysis of a mathematical model for the growth of tumors ［J］. Journal of Mathematical Biology， 1999， 38（3）： 262-284.

CUI S， FRIEDMAN A. Analysis of a mathematical model of the effect of inhibitors on the growth of tumors ［J］. Mathematical Biosciences， 2000， 164（2）： 103-137.

CUI S， FRIEDMAN A. A hyperbolic free boundary problem modeling tumor growth ［J］. Interfaces & Free Boundaries， 2003， 5（2）： 159-181.

CUI S. Analysis of a mathematical model for the growth of tumors under the action of external inhibitors ［J］. Journal of Mathematical Biology， 2002， 44（5）： 395-426.

CUI S. Analysis of a free boundary problem modeling tumor growth ［J］. Acta Mathematica Sinica， 2005， 21（5）： 1071-1082.

卫雪梅，崔尚斌. 一个肿瘤生长自由边界问题解的整体存在性和唯一性［J］. 数学物理学报， 2006， 26（1）： 1-8.

卫雪梅，崔尚斌. 一个肿瘤生长自由边界问题解的渐近性态［J］. 数学物理学报， 2007， 27（4）： 648-659.

CUI S B， WEI X M. Global existence for a parabolic-hyperbolic free boundary problem modelling tumor growth ［J］. Acta Mathematicae Applicatae Sinica （English series）， 2005， 21（4）： 597-614.

CUI S， FRIEDMAN A. Analysis of a mathematical model of the growth of necrotic tumors ［J］. Journal of Mathematical Analysis and Applications， 2001， 255（2）： 636-677.

WEI X. Global existence for a free boundary problem modelling the growth of necrotic tumors in the presence of inhibitors ［J］. International Journal of Pure and Applied Mathematics， 2006， 28（3）： 321-338.

FRIEDMAN A， LAM K Y. Analysis of a free-boundary tumor model with angiogenesis ［J］. Journal of Differential Equations， 2015， 259（12）： 7636-7661.

SHEN H， WEI X. A qualitative analysis of a free boundary problem modeling tumor growth with angiogenesis ［J］. Nonlinear Analysis： Real World Applications， 2019， 47： 106-126.

ZHUANG Y， CUI S. Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis ［J］. Journal of Differential Equations， 2018， 265（2）： 620-644.

ZHENG J， CUI S. Analysis of a tumor model free boundary problem with action of an inhibitor and nonlinear boundary conditions ［J］. Journal of Mathematical Analysis and Applications， 2021， 496（1）： 124793.

沈海双，卫雪梅，刘成霞，等. 具有第三边界坏死核肿瘤数学模型稳态解的存在唯一性［J］. 中山大学学报（自然科学版）， 2018， 57（5）： 140-144.

XU S， SU D. Analysis of necrotic core formation in angiogenic tumor growth ［J］. Nonlinear Analysis： Real World Applications， 2020， 51： 103016.

SONG H， HU W， WANG Z. Analysis of a nonlinear free-boundary tumor model with angiogenesis and a connection between the nonnecrotic and necrotic phases ［J］. Nonlinear Analysis： Real World Applications， 2021， 59： 103270.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Analysis of a Mathematical Model of the Response of Spatially Structured Tumors to Chemotherapy Model

Analysis of a Mathematical Modeling of Cancer Cell Breakout and #br# Invasion of Normal Tissue or Extracellular Matrix

Existence and Uniqueness of Global Solution for a Model of Immune Cells Inhibiting Tumor Immune Evasion

Well-posedness for a Free Boundary Problem Modeling Protocells

Related Author

Xuemei WEI

Zhaoyong FENG

Chengxia LIU

Die HU

FENG Zhaoyong

WEI Xuemei

GAO Shuaishuai

WEI Xuemei

Related Institution

School of Applied Mathematics， Guangdong University of Technology

School of Mathematics and Computational Science, Sun Yat-sen University

Institute of Applied Mathematics, Guangdong University of Technology

School of Mathematics and Computational Science, Sun Yatsen University, Guangzhou



Postal code：510275
Tel：020-84112585，84113223 Email：xuebaozr@mail.sysu.edu.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备09064830号-19 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰