论文标题
当自我生成的梯度与细胞分裂和扩散相互作用时。最小模型的分析
When Self-Generated Gradients interact with Expansion by Cell Division and Diffusion. Analysis of a Minimal Model
论文作者
论文摘要
我们研究了一个最小的细胞传播模型，该模型涉及沿着自生成的信号传导梯度和细胞分裂迁移，该模型已在早期研究中提出。该模型由两个耦合抛物线扩散 - 辅助反应方程的系统组成。由于不连续的对流术语，应谨慎处理库奇问题。我们首先在信号传导梯度上的单调条件下，在当地建立了本地的存在和唯一性，通过将问题减少到颂歌的良好性。然后，我们对系统进行渐近分析。计算系统的所有正和有限的行进波，并推导最小波速的明确公式。对波的内部动力学的分析，根据对流的强度在推动波和拉动波之间建立了二分法。我们将最小波速度确定为弱意义上的生物学相关速度，即，溶液的传播速度分别比最小的波速更快地传播，直到时间提取。最后，我们将研究扩展到具有持久性的双曲线两速度模型。
We investigate a minimal model for cell propagation involving migration along self-generated signaling gradients and cell division, which has been proposed in an earlier study. The model consists in a system of two coupled parabolic diffusion-advection-reaction equations. Because of a discontinuous advection term, the Cauchy problem should be handled with care. We first establish existence and uniqueness locally in time through the reduction of the problem to the well-posedness of an ODE, under a monotonicity condition on the signaling gradient. Then, we carry out an asymptotic analysis of the system. All positive and bounded traveling waves of the system are computed and an explicit formula for the minimal wave speed is deduced. An analysis on the inside dynamics of the wave establishes a dichotomy between pushed and pulled waves depending on the strength of the advection. We identified the minimal wave speed as the biologically relevant speed, in a weak sense, that is, the solution propagates slower, respectively faster, than the minimal wave speed, up to time extraction. Finally, we extend the study to a hyperbolic two-velocity model with persistence.
