Abstract A logarithmic model type chemotaxis equation is introduced with porous medium diffusion and a population dependent consumption rate. The classical assumption that individual bacterium can sense the chemical gradient is not taken. Instead, the chemotactic term appears by assuming that the migration distance is inversely proportional to the amount of food if food is the reason for migration. The existence and uniqueness of a traveling wave solution of the model are obtained. In particular, solutions have interfaces that divide into constant and non-constant regions. In particular, the profile of the population distribution has compact support. Numerical simulations are provided and compared with analytic results.

中文翻译：

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具有紧凑支撑的趋化行波

摘要 引入了多孔介质扩散和种群相关消耗率的对数模型型趋化方程。没有采用单个细菌可以感知化学梯度的经典假设。相反，如果食物是迁移的原因，则通过假设迁移距离与食物量成反比而出现趋化项。得到了模型行波解的存在唯一性。特别是，解决方案具有分为恒定区和非恒定区的接口。特别是，人口分布的轮廓具有紧凑的支持。提供了数值模拟并与分析结果进行了比较。