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

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.