摘要
该文研究一类基于凋亡调节机制含时滞的血管化肿瘤生长模型自由边界问题,其中参数σ_(∞)、、σ_(h)分别表示在肿瘤周围组织中的营养物浓度、细胞有丝分裂所需的营养物浓度阈值、凋亡调节机制被激活的营养物浓度阈值.当σ_(∞)<<σ_(h)时,利用时滞微分方程经典理论建立了正稳态解的存在唯一性及稳定性.研究结果表明:区别于不含有凋亡调节机制的肿瘤生长模型,即使在营养物供应不足的情况下正稳态解仍存在且稳定.最后,借助数值模拟验证了在拟稳态下稳态解的存在唯一性与稳定性.
In this paper,the free boundary problem modeling the growth of vascularized tumors with time delays in regulatory apoptosis is studied,whereσ_(∞),,σ_(h)denote the nutrient concentration outside the tumor,the threshold of the nutrient concentration for cell mitosis and the threshold for the regulatory mechanism,respectively.Using the classical theory of delay differential equations,the existence,uniqueness,stability of positive stationary solution are established under the assumption thatσ_(∞)<<σ_(h).The results show that compared with the tumor growth model wi-thout apoptotic regulation mechanism,the positive stationary solution still exists and stable even under the condition of insufficient nutrient supply.Finally,the existence,uniqueness and stability of the stationary solution in quasi-stationary case are verified by numerical simulations.
作者
刘亚新
龙荃
王泽佳
LIU Yaxin;LONG Quan;WANG Zejia(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China;The High School Affiliated to Gannan Normal University,Ganzhou Jiangxi 341000,China)
出处
《江西师范大学学报(自然科学版)》
北大核心
2025年第2期204-212,共9页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
国家自然科学基金(11861038,12161045,12251047)资助项目.
关键词
血管化肿瘤
自由边界
凋亡调节机制
时滞
稳定性
vascularized tumor
free boundary
regulatory mechanism of apoptosis
time delay
stability
