In this letter we present a Keller–Segel model with logistic growth dynamics arising in the study of chemotactic pattern formation. We prove the existence of a minimum wave speed for which the model exhibits nonnegative traveling wave solutions at all speeds above this value and none below. The exact value of the minimum wave speed is given for all biologically relevant parameter values. These results strengthen recent results where non-sharp upper and lower bounds on the minimum wave speed were derived in a restricted parameter regime.

中文翻译：

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Keller-Segel模型中的行波精确最小速度

在这封信中，我们提出了一种Keller-Segel模型，该模型具有在趋化模式形成研究中出现的逻辑增长动态。我们证明了最小波速的存在，对于该最小波速，该模型在高于此值的所有速度下均显示非负行波解，而低于该速度时则不存在。给出所有生物学相关参数值的最小波速的准确值。这些结果加强了最近的结果，其中在受限参数范围内得出了最小波速的非锐利上限和下限。