A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary

Zhou Yun; Wei Xue-mei

doi:10.12052/gdutxb.200109

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary

更新时间：2026-05-27

- A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary
- Vol. 38, Issue 2, Pages: 60-65(2021)
- 作者机构：
  
  广东工业大学应用数学学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.200109
  CLC： O175
- Online First：10 March 2021，
  
  Published：2021
- 稿件说明：
移动端阅览
周云, 卫雪梅. 一个具有Robin自由边界的双曲肿瘤生长模型解的定性分析[J]. 广东工业大学学报, 2021, 38(2): 60-65.

Zhou Yun, Wei Xue-mei. A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary[J]. 2021, 38(2): 60-65.
周云, 卫雪梅. 一个具有Robin自由边界的双曲肿瘤生长模型解的定性分析[J]. 广东工业大学学报, 2021, 38(2): 60-65. DOI： 10.12052/gdutxb.200109.

Zhou Yun, Wei Xue-mei. A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary[J]. 2021, 38(2): 60-65. DOI： 10.12052/gdutxb.200109.

摘要

研究了一个具有Robin自由边界的双曲肿瘤生长数学模型

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描述肿瘤细胞生长的两个双曲型偏微分方程。本文通过特征线方法结合

${\rm{Banach}}$

img text_id='M1' class='formula-img' style='display:none;' src='gdgydxxb-38-2-60_M1.jpg'>

不动点定理证明了该模型整体解的存在性和唯一性。最后证明当

${K_R} = 0$

img text_id='M2' class='formula-img' style='display:none;' src='gdgydxxb-38-2-60_M2.jpg'>

时

有

$\mathop {\lim }\limits_{t \to \infty } R\left( t \right) = \infty $

img text_id='M3' class='formula-img' style='display:none;' src='gdgydxxb-38-2-60_M3.jpg'>

。

Abstract

A hyperbolic tumor growth model with Robin free boundary is studied

which contains an elliptic partial differential equation describing the concentration of nutrients

an ordinary differential equat

ion describing the radius of tumor and two hyperbolic equations describing the growth of tumor cells. In this paper

by applying the method of characteristic curves and the Banach fixed point theorem

the existence and uniqueness of the global solution of the model are proven. Finally

it is proven that while

${K_R} = 0$

img text_id='M4' class='formula-img' style='display:none;' src='gdgydxxb-38-2-60_M4.jpg'>

$\mathop {\lim }\limits_{t \to \infty } R\left( t \right) = \infty$

img text_id='M5' class='formula-img' style='display:none;' src='gdgydxxb-38-2-60_M5.jpg'>

关键词

Keywords

references

CUI S B. Free boundary problems modeling tumor growth [J]. Advances in Mathematics, 2009, 38(1): 1-18.

DRASDO D, HÖHME S. A single cell based model of tumor growth in vitro: monolayers [J]. Physical Biology, 2005, 2(3): 133.

KIM J B, STEIN R, O'HARE M J. Three-dimensional in vitro tissue culture models for breast cancer-a review [J ] . Breast Cancer Research Treatment, 2004, 85(3): 281-291.

KYLE A H, CHAN C T O, MINCHINTON A I. Characterization of three-dimensional tissue cultures using impedance spectroscopy [J]. Biophysical Journal, 1999, 76(5): 2640-2648.

MUELLER-KLIESER W. Three-dimensional cell cultures: from molecular mechanisms to clinical applications [J]. American Journal of Physiology Cell Physiology, 1997, 273(4): 1109-1123.

ADAM J A, BELLOMO N. A survey of models for tumor-immune system dynamics[M]. Boston: Birkhäuser, 1997: 89-133.

SUTHERLAND R M. Cell and enviroment interactions in tumor microregions: the multicell spheroid model [J]. Science, 1998, 240(4849): 177-184.

CUI S B, FRIEDMAN A. A hyperbolic free boundary problem modeling tumor growth [J]. Interfaces and Free Boundaries, 2003, 5(2): 159-182.

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

WEI X M, CUI S B. Global well-posedness for a drug transport model in tumor multicell spheroids [J]. Mathematical Computer Modelling, 2007, 45(5-6): 553-563.

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

沈海双. 带有Robin 自由边界条件的肿瘤生长模型的定性分析[D]. 广州: 广东工业大学, 2019.

PETTET G J, PLEASE C P, TINDALL M J, et al . The migration of cells in multicell tumor spheroids [J ] . Bulletin of Mathematical Biology, 2001, 63(2): 231-257.

PROTTER M H, WEINBERGER H F. Maximum Principles in Differential Equations[M]. New York: Springer, 1967: 1-3.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Existence and Uniqueness of Global Solution to a Mathematical Model of Retinal Vascular Tumors

Existence and Uniqueness of Global Solution for a Model of Retinal Oxygen Distribution and the Role of Neuroglobin

Existence of the Solution to the Metabolic Model of Colon Cancer Cells

Modeling of 3D NAND Memory Cells with Taper Angle and Programming Strategy Optimization

Bimodal Iterative Cross-attention Fusion Ensemble Framework

Related Author

Lu Chuang-ye

Wei Xue-mei

Chen Mei-gui

Wei Xue-mei

Liang Xiao-zhen

Related Institution

School of Applied Mathematics, Guangdong University of Technology

AI问答

⁰