血管化肿瘤生长自由边界问题全局解的存在唯一性
Existence and Uniqueness of Global Solutions of a Free Boundary Problem Modeling Tumor Growth with Angiogenesis
摘要: 本文研究一个含抑制剂的血管型肿瘤生长模型。该模型包含了一个描述肿瘤半径的常微分方程和两个分别描述营养物浓度和抑制物浓度变化的抛物型方程。通过运用抛物型方程的 理论、边界固定法和Banach不动点定理，证明了该问题局部解的存在唯一性，然后用延拓方法得到了整体解的存在唯一性。
Abstract: The vascularized tumor growth model with inhibitor was studied. The model consists an ordinary differential equation describing tumor radius, and two parabolic equations describing the variation of nutrients and inhibitor concentrations, respectively. By applying the theory of parabolic equations, the boundary fixation method and the Banach fixed point theorem, the existence and uniqueness of a local solution was proved, and then the extension method was used to obtain the existence and uniqueness of the global solution.
文章引用：盖梦琳, 朱妍红. 血管化肿瘤生长自由边界问题全局解的存在唯一性[J]. 应用数学进展, 2023, 12(12): 5202-5209. https://doi.org/10.12677/AAM.2023.1212511

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