论文标题
与坏死核和趋化性血管肿瘤生长的自由边界模型的分叉分析
Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis
论文作者
论文摘要
大量的研究作品专门研究肿瘤模型的研究。已经发现几种生物物理因素，例如细胞增殖，凋亡，趋化性，血管生成和坏死，对复杂的肿瘤生物系统产生了影响。肿瘤发育侵略性的指标是肿瘤边界形状的不稳定性。 LU，Min-Jhe等人已经探索了肿瘤形态的复杂模式。 [通过趋化性和坏死控制血管肿瘤生长的非线性模拟，计算物理学杂志459（2022）：111153]。在本文中，我们继续对具有受控坏死核心和趋化性的血管肿瘤模型进行分叉分析。该分叉分析是针对细胞增殖的参数，建立在径向对称稳态溶液的显式公式上。通过扰动肿瘤无边界并建立了自由边界系统的严格估计，应用了hanzawa转换的％，我们证明了具有Crandall-Rabinowitz定理的分叉分支的存在。发现趋化性的参数会影响分叉点的单调性，因为模式$ l $在理论上和数值上都增加。
A considerable number of research works has been devoted to the study of tumor models. Several biophysical factors, such as cell proliferation, apoptosis, chemotaxis, angiogenesis and necrosis, have been discovered to have an impact on the complicated biological system of tumors. An indicator of the aggressiveness of tumor development is the instability of the shape of the tumor boundary. Complex patterns of tumor morphology have been explored by Lu, Min-Jhe et al. [Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis, Journal of Computational Physics 459 (2022): 111153]. In this paper, we continue to carry out a bifurcation analysis on such a vascular tumor model with a controlled necrotic core and chemotaxis. This bifurcation analysis, to the parameter of cell proliferation, is built on the explicit formulas of radially symmetric steady-state solutions. By perturbing the tumor free boundary and establishing rigorous estimates of the free boundary system, %applying the Hanzawa transformation, we prove the existence of the bifurcation branches with Crandall-Rabinowitz theorem. The parameter of chemotaxis is found to influence the monotonicity of the bifurcation point as the mode $l$ increases both theoretically and numerically.
