In this work, we develop a model to describe some aspects of communication between yeast cells. It consists in a coupled system of two one-dimensional non-linear advection-diffusion equations in which the advective field is given by the Hilbert transform. We give some sufficient condition for the blow-up in finite time of the coupled system (formation of a singularity). We provide a biological interpretation of these mathematical results.

中文翻译：

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一种非线性系统，用于模拟酵母细胞在交配过程中之间的通信

在这项工作中，我们开发了一个模型来描述酵母细胞之间通信的某些方面。它由两个一维非线性平流扩散方程的耦合系统组成，其中平流场由希尔伯特变换给出。我们给出了耦合系统在有限时间内爆炸（奇点的形成）的一些充分条件。我们对这些数学结果提供了生物学解释。