具周期营养供给的血管化肿瘤生长模型的渐近分析

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 261-273.

具周期营养供给的血管化肿瘤生长模型的渐近分析

宋慧娟¹,黄倩²,王泽佳^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

Song Huijuan¹,Huang Qian²,Wang Zejia^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)

摘要/Abstract

摘要：

该文考虑具 $\omega$ -周期营养 $\phi(t)$ 供给的血管化肿瘤生长模型自由边界问题, 其中肿瘤细胞繁衍速率函数为 $S(\sigma)$. 对此问题, 该文首先建立了适定性, 其次, 根据 $\frac1{\omega}\int^{\omega}_0S(\phi(t)){\rm d}t$ 的符号对解的渐近性态给出了完整分类, 即若 $\frac1{\omega}\int^{\omega}_0S(\phi(t)){\rm d}t\le0$, 则所有肿瘤将最终消失, 反之亦然; 若 $\frac1{\omega}\int^{\omega}_0S(\phi(t)){\rm d}t>0$, 则问题存在唯一的稳定的正周期解.

关键词: 自由边界问题, 含有死核的肿瘤, 血管生成, 周期解, 稳定性

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.

Key words: Free boundary problem, Necrotic tumor, Angiogenesis, Periodic solution, Stability

中图分类号:

O175

宋慧娟, 黄倩, 王泽佳. 具周期营养供给的血管化肿瘤生长模型的渐近分析[J]. 数学物理学报, 2023, 43(1): 261-273.

Song Huijuan, Huang Qian, Wang Zejia. Asymptotic Analysis of a Tumor Model with Angiogenesis and a Periodic Supply of External Nutrients[J]. Acta mathematica scientia,Series A, 2023, 43(1): 261-273.

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