[1]张 钦,王泽佳*.环柱状血管化肿瘤生长模型的自由边界问题[J].江西师范大学学报(自然科学版),2020,(01):12-16.[doi:10.16357/j.cnki.issn1000-5862.2020.01.03]
　ZHANG Qin,WANG Zejia*.The Free Boundary Problem Modeling the Growth of Tumor Cord with Angiogenesis[J].Journal of Jiangxi Normal University:Natural Science Edition,2020,(01):12-16.[doi:10.16357/j.cnki.issn1000-5862.2020.01.03]
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环柱状血管化肿瘤生长模型的自由边界问题()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2020年01期
页码:
12-16
栏目:
数学与应用数学
出版日期:
2020-02-10

文章信息/Info

Title:
The Free Boundary Problem Modeling the Growth of Tumor Cord with Angiogenesis
文章编号:
1000-5862(2020)01-0012-05
作者:
张 钦; 王泽佳*
江西师范大学数学与信息科学学院,江西 南昌 330022
Author(s):
ZHANG Qin; WANG Zejia*
College of Mathematics and Information Science,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
环柱状肿瘤;  自由边界;  稳态解;  径向对称解
Keywords:
tumor cord;  free boundary;  stationary solution;  radially symmetric solution
分类号:
O 175.29
DOI:
10.16357/j.cnki.issn1000-5862.2020.01.03
文献标志码:
A
摘要:
该文研究环柱状血管化肿瘤生长模型的自由边界问题. 假设肿瘤环绕血管外侧生长,考虑其垂直截面的生长规律.肿瘤区域的内侧边界是固定的,外侧边界是自由边界.证明了:(i)该问题存在稳态解;(ii)若血管化函数α(t)保持一致有界,则自由边界R(t)保持一致有界;(iii)若limt→∞α(t)=0,则自由边界将收缩至内边界,即肿瘤消失.
Abstract:
In this paper,the free boundary problem modeling the growth of tumor cord with angiogenesis is studied.Assuming that the tumor grows along the outside of blood vessel,the domain of tumor considered has two boundary,the inside boundary is fixed and the outside is free.For this problem,It is proved that there is a radially stationary solution to the problem.If the angiogenesis function α(t) is uniformly bounded,then the free boundary R(t) is uniformly bounded.If limt→∞ α(t)=0,the free boundary will shrink to the inner boundary,that is,the tumor disappears.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2019-11-10
基金项目:国家自然科学基金(11861038)和江西省教育厅基金(GJJ160299)资助项目.
通信作者:王泽佳(1979-),女,黑龙江安达人,教授,博士,博士生导师,主要从事非线性偏微分方程理论及其应用方面的研究.E-mail:zejiawang@jxnu.edu.cn
更新日期/Last Update: 2020-02-10