广东工业大学学报 ›› 2021, Vol. 38 ›› Issue (02): 60-65.doi: 10.12052/gdutxb.200109

• 综合研究 • 上一篇    下一篇

一个具有Robin自由边界的双曲肿瘤生长模型解的定性分析

周云, 卫雪梅   

  1. 广东工业大学 应用数学学院, 广东 广州 510520
  • 收稿日期:2020-08-28 出版日期:2021-03-10 发布日期:2021-01-13
  • 通信作者: 卫雪梅(1972-),女,教授,硕士生导师,主要研究方向为偏微分方程,E-mail:wxm_gdut@163.com E-mail:wxm_gdut@163.com
  • 作者简介:周云(1995-)，女，硕士研究生，主要研究方向为偏微分方程
  • 基金资助:
    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)

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

Zhou Yun, Wei Xue-mei   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2020-08-28 Online:2021-03-10 Published:2021-01-13

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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${\rm{Banach}}$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${K_R} = 0$时, 有$\mathop {\lim }\limits_{t \to \infty } R\left( t \right) = \infty $。

关键词: 肿瘤生长, 自由边界问题, 整体解

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 equation 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 ${K_R} = 0$, $\mathop {\lim }\limits_{t \to \infty } R\left( t \right) = \infty$.

Key words: tumor growth, free boundary problem, global solution

中图分类号: 

  • O175
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