结肠癌细胞代谢模型解的存在性

梁小珍; 卫雪梅

doi:10.12052/gdutxb.180177

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结肠癌细胞代谢模型解的存在性

综合研究 | 更新时间：2026-05-27

- 结肠癌细胞代谢模型解的存在性
- Existence of the Solution to the Metabolic Model of Colon Cancer Cells
- 广东工业大学学报 2019年36卷第5期页码：38-42
- 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：
  
  梁小珍(1992−)，女，硕士研究生，主要研究方向为偏微分方程
  卫雪梅(1972−)，女，教授，主要研究方向为偏微分方程. E-mail：wxm_gdut@163.com
- 基金信息：
  
  国家自然科学基金资助项目(11101095);广东省高校特色创新类项目(2016KTSCX028);广东省高层次人才项目(2014011);研究生教育创新项目(2014QTLXXM17)
- DOI：10.12052/gdutxb.180177
  中图分类号： O175
- 网络首发：2019-08-21，
  
  纸质出版：2019
- 稿件说明：
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梁小珍, 卫雪梅. 结肠癌细胞代谢模型解的存在性[J]. 广东工业大学学报, 2019, 36(5): 38-42.

Liang Xiao-zhen, Wei Xue-mei. Existence of the Solution to the Metabolic Model of Colon Cancer Cells[J]. 2019, 36(5): 38-42.
梁小珍, 卫雪梅. 结肠癌细胞代谢模型解的存在性[J]. 广东工业大学学报, 2019, 36(5): 38-42. DOI： 10.12052/gdutxb.180177.

Liang Xiao-zhen, Wei Xue-mei. Existence of the Solution to the Metabolic Model of Colon Cancer Cells[J]. 2019, 36(5): 38-42. DOI： 10.12052/gdutxb.180177.

摘要

研究了结肠癌细胞代谢数学模型. 该模型由包含不连续项的5个相互耦合的反应扩散方程组成. 本文运用抛物型方程的

理论和Schauder不动点定理以及逼近方法证明了该数学模型整体解的存在性.

Abstract

The metabolic model of colon cancer cells is studied. The model contains five coupled reaction diffusion equations

in which some equations involve discontinuous terms. It is proved that this problem has a global solution by using the

-theory for parabolic equations

the Schauder Fixed Point Theorem and approximation method.

关键词

Keywords

references

YANG Q, XIA L P. Research progress of metabolic symbiosis in cancer [J]. Chinese Clinical Oncology, 2015, 20(4): 371-375.

PENKERT J, RIPPERGER T, SCHIECK M, et al . On metabolic reprogramming and tumor biology: A comprehensive survey of metabolism in breast cancer [J ] . Oncotarget, 2016, 7(41): 67626-67649.

LAURA P, RUBEN B, EMESTA F, et al . Targeting metabolic symbiosis to overcome resistance to antiangiogenic therapy [J ] . Cell Reports, 2016, 15(6): 1161-1174.

CHAE Y C, KIM J H. Cancer stem cell metabolism: target for cancer therapy [J]. Bmb Reports, 2018, 51(7): 319-326.

VAN D C, KIM J W. Convergence of cancer metabolism and immunity: an overview [J]. Biomoles Therapeutics, 2018, 26(1): 4-9.

MENDOZA-JUEZ B, CALVO G F, VICTOR M, et al . A mathematical model for the glucoselactate metabolism of in vitro cancer cells [J ] . Bulletin of Mathematical Biology, 2012, 74(5): 1125-1142.

MCGILLEN J B, KELLY C J, GAFFNEY E A, et al . Glucose-lactate metabolic cooperation in cancer: Insights from a spatial mathematical model and implications for targeted therapy [J ] . Journal of Theoretical Biology, 2014, 361(1): 190-203.

LEE M, CHEN G T, PUTTOCK E, et al . Mathematical modeling links Wnt signaling to emergent patterns of metabolism in colon cancer [J ] . Molecular Systems Biology, 2017, 13(2): 912.

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

Cui S B. Formation of necrotic cores in the growth of tumors: analytic results [J]. Acta Mathematica Scientia, 2006, 26B(4): 781-796.

姜礼尚, 陈亚浙. 数学物理方程讲义[M]. 北京: 高等教育出版社, 2007.

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

CUI S B. Existence of a stationary solution for the modified king-ward tumor growth model [J]. Advances in Applied Mathematics, 2006, 36(4): 421-445.

CUI S B. Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors [J]. Interfaces Free Boundaries, 2005, 7(2): 147-159.

WEI X M, GUO C H. Global existence for a mathematical model of the immune response to cancer [J]. Nonlinear Analysis Real World Applications, 2010, 11(5): 3903-3911.

CHEN M G, WEI X M. Existence and uniqueness of global solution for a model of retinal oxygen distribution and the role of neuroglobin [J]. Journal of Guangdong University of Technology, 2018, 35(5): 45-50.

LU C Y, WEI X M. Existence and uniqueness of global solution to a mathematical model of retinal vascular tumors [J]. Journal of Guangdong University of Technology, 2016, 33(3): 70-75.

崔尚斌. 偏微分方程现代理论引论[M]. 北京: 科学出版社, 2015.

LADYZENSKAJA O A, SOLONNIKOV V A, URALCEVA N N. Linear and quasilinear partial differential equations of parabolic type, translations of mathematical monographs[M]. Providence: Amer Math Soc, 1968, 23.

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