论文标题
在细胞极化模型中产生的抛物线无界边界问题
A parabolic free boundary problem arising in a model of cell polarization
论文作者
论文摘要
外部信号的扩增是生物细胞方向传感的关键步骤。我们考虑了一个简单的模型，用于响应时间扩展信号，该模型以前是最后三位作者提出的。该模型由散装表面反应扩散模型组成。我们证明，在合适的渐近限制中，系统会收敛到散装抛物线障碍物类型问题。对于此模型，并减少了非局部表面方程，我们显示了L1征收特性，在时间稳定信号的情况下，我们显示了固定状态的稳定性。
The amplification of an external signal is a key step in direction sensing of biological cells. We consider a simple model for the response to a time-depending signal, which was previously proposed by the last three authors. The model consists of a bulk-surface reaction-diffusion model. We prove that in a suitable asymptotic limit the system converges to a bulk-surface parabolic obstacle type problem. For this model and a reduction to a nonlocal surface equation we show an L1-contraction property and, in the case of time-constant signals, the stability of stationary states.
