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### 具周期营养供给的血管化肿瘤生长模型的渐近分析

1. 1江西师范大学数学与统计学院 南昌330022
2广丰中学 江西上饶334699
• 收稿日期:2021-11-24 修回日期:2022-07-05 出版日期:2023-02-26 发布日期:2023-03-07
• 通讯作者: *王泽佳, E-mail: zejiawang@jxnu.edu.cn
• 基金资助:
国家自然科学基金(12261047);国家自然科学基金(12161045);国家自然科学基金(11861038);江西省自然科学基金(20212BAB201016)

### Asymptotic Analysis of a Tumor Model with Angiogenesis and a Periodic Supply of External Nutrients

Huijuan Song1,Qian Huang2,Zejia Wang1,*()

1. 1School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
2Guangfeng Middle School, Jiangxi Shangrao 334699
• Received:2021-11-24 Revised:2022-07-05 Online:2023-02-26 Published:2023-03-07
• Supported by:
The NSFC(12261047);The NSFC(12161045);The NSFC(11861038);Natural Science Foundation of Jiangxi Province of China(20212BAB201016)

Abstract:

In this paper, we consider a free boundary problem modeling the growth of tumors with angiogenesis and a $\omega$-periodic supply of external nutrients $\phi(t)$. Denote by $S(\sigma)$ the proliferation rate of tumor cells. We first establish the well-posedness and then give a complete classification of asymptotic behavior of solutions according to the sign of $\frac1{\omega}\int_0^\omega S(\phi(t)){\rm d}t$. It is shown that if $\frac1{\omega}\int_0^\omega S(\phi(t)){\rm d}t\le0$, then all evolutionary tumors will finally vanish; the converse is also true. If instead $\frac1{\omega}\int_0^\omega S(\phi(t)){\rm d}t>0$, then there exists a unique and stable positive periodic solution.

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