模拟细胞极化的质量守恒自由边界问题解的界面行为
Interface behavior for the solutions of a mass conserving free boundary problem modeling cell polarization
AI总结：
本文研究模拟细胞极化的质量守恒自由边界问题，在轴对称及单调性假设下证明自由边界全局连续，并揭示违反“无增厚”条件时边界在初始时刻可振荡。
摘要：
我们考虑一个抛物型非局部自由边界问题，该问题作为模拟细胞极化的体-表面反应-扩散系统的极限而导出。在之前的论文中，我们建立了该问题的适定性，并导出了初始数据条件以保证自由边界在 $t\ o 0$ 时的连续性。在本文中，我们通过考虑轴对称数据来扩展自由边界的定性研究。在数据的额外单调性假设下，我们证明了自由边界的全局连续性。另一方面，如果初始数据违反“无增厚”条件，我们表明自由边界在 $t \ o 0$ 时可能振荡。
英文摘要：
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. In previous papers, we have established well-posedness of this problem and derived conditions on the initial data that imply continuity of the free boundary as $t\to 0$. In this paper we extend the qualitative study of the free boundary by considering axisymmetric data. Under additional monotonicity assumptions on the data we prove global continuity of the free boundary. On the other hand, if the initial data violate a "no-fattening" condition we show that the free boundary can oscillate as $t \to 0$.
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