摘要
研究一个营养物和抑制物同时存在的非线性血管化肿瘤生长模型.首先运用边界固定法将自由边界问题转化为固定边界上的非线性初边值问题,其次运用抛物型方程的L^(p)理论和Banach不动点定理构造压缩映射,证明该问题局部解的存在唯一性,最后利用变换函数与其原始函数之间的关系,用延拓方法得到整体解的存在唯一性.
The nonlinear vascular tumor growth model with simultaneous presence of nutrients and inhibitors was studied.The boundary fixation method was applied to transform the free boundary problem into a nonlinear initial margin value problem on a fixed boundary.By applying the L^(p)theory of parabolic equations and the Banach fixed point theorem to construct a compression mapping,the existence and uniqueness of the local solution was proved,and then the relationship between the transformed function and its primal function was used to obtain the existence and uniqueness of the global solution by using the extension method.
作者
宋灵宇
盖梦琳
朱妍红
SONG Ling-yu;GE Meng-lin;ZHU Yan-hong(School of Science,Chang an University,Xi'an 710064,Shaanxi,China)
出处
《西北师范大学学报（自然科学版）》
2024年第1期14-19,共6页
Journal of Northwest Normal University(Natural Science)
基金
国家自然科学青年基金资助项目(12101482)
中国博士后科学基金面上资助项目(2022M722604)
陕西省科技厅重点研发一般资助项目(2023-YBSF-372)。
关键词
肿瘤生长模型
自由边界问题
整体解
存在性
唯一性
tumor growth model
free boundary problem
global solution
existence
uniqueness
