具周期营养供给的血管化肿瘤生长模型的渐近分析  

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

作　　者：宋慧娟[1] 黄倩 王泽佳 Huijuan Song;Qian Huang;Zejia Wang(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022;Guangfeng Middle School,Jiangxi Shangrao 334699)

机构地区：[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

出　　处：《数学物理学报（A辑）》2023年第1期261-273,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(12261047,12161045,11861038);江西省自然科学基金(20212BAB201016)。

摘　　要：该文考虑具w-周期营养Φ(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(σ).对此问题,该文首先建立了适定性,其次,根据1/w∫0wS(Φ(t))dt的符号对解的渐近性态给出了完整分类,即若1/w∫0wS(Φ(t))dt≤0,则所有肿瘤将最终消失,反之亦然;若1/w∫0wS(Φ(t))dt> 0,则问题存在唯一的稳定的正周期解.In this paper,we consider a free boundary problem modeling the growth of tumors with angiogenesis and a w-periodic supply of external nutrients Φ(t).Denote by S(a) 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 1/w∫0wS(Φ(t))dt.It is shown that if 1/w∫0wS(Φ(t))dt≤0,then all evolutionary tumors will finally vanish;the converse is also true.If instead 1/w∫0wS(Φ(t))dt> 0,then there exists a unique and stable positive periodic solution.

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 

分 类 号：O175[理学—数学]