The aim of this paper is to elucidate the existence of patterns for Keller–Segel-type models that are solutions of the traveling pulse form. The idea is to search for transport mechanisms that describe this type of waves with compact support, which we find in the so-called nonlinear diffusion through saturated flux mechanisms for the movement cell. At the same time, we analyze various transport operators for the chemoattractant. The techniques used combine the analysis of the phase diagram in dynamic systems together with its counterpart in the system of partial differential equations through the concept of entropic solution and the admissible jump conditions of the Rankine–Hugoniot type. We found traveling pulse waves of two types that correspond to those found experimentally.

本文的目的是阐明 Keller-Segel 型模型的模式的存在性，这些模型是行进脉冲形式的解决方案。这个想法是寻找描述这种具有紧凑支撑的波的传输机制，我们在所谓的通过运动单元的饱和​​通量机制的非线性扩散中发现了这种机制。同时，我们分析了化学引诱剂的各种运输运营商。所使用的技术通过熵解的概念和朗肯-于戈尼奥类型的允许跳跃条件，将动态系统中的相图分析与偏微分方程组中的对应分析结合起来。我们发现了两种类型的行波脉冲波，与实验中发现的脉冲波相对应。