压力反馈诱导的肿瘤边界不稳定性
Tumor boundary instability induced by pressure feedback
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中文总结 AI 辅助
本研究针对由多孔介质方程不可压缩极限导出的Hele–Shaw型肿瘤生长模型，通过渐近分析推导稳定性判据，发现压力反馈可在无压力反馈时稳定的参数范围诱导肿瘤边界不稳定性。
中文摘要 AI 辅助
我们研究一类Hele–Shaw型肿瘤生长模型，该模型由多孔介质方程的不可压缩极限导出。该极限模型保留肿瘤密度的斑块结构，因此可采用单一自由边界形式表述。我们探究与稳态压力相关的压力反馈参数如何影响边界稳定性，通过渐近分析研究有限半径肿瘤及平面行波前的边界扰动，推导相应稳定性判据。对于平面行波前，进一步证明其稳定性阈值为分岔点，非对称行波由此产生。结果表明，在无压力反馈时模型仍保持稳定的参数范围内，压力反馈可诱导边界不稳定性。
英文摘要
We consider a Hele--Shaw-type tumor growth model obtained from the incompressible limit of a porous-medium equation. The limiting model preserves the patch structure of the tumor density and therefore admits a single free-boundary formulation. We investigate how a pressure-feedback parameter associated with the homeostatic pressure affects boundary stability. Using asymptotic analysis, we study boundary perturbations of finite-radius tumors and planar traveling fronts and derive the corresponding stability criteria. For planar fronts, the stability thresholds are further shown to be bifurcation points from which nonsymmetric traveling waves emerge. Our results indicate that pressure feedback can induce boundary instability in parameter regimes where the model without pressure feedback remains stable.
发表机构
- Great Bay University（大湾区大学）
- Shanghai University of Finance and Economics（上海财经大学）
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