环柱状血管化肿瘤生长模型的自由边界问题
The Free Boundary Problem Modeling the Growth of Tumor Cord with Angiogenesis

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.
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