Exact minimum speed of traveling waves in a Keller--Segel model

TL;DR

This paper determines the exact minimum wave speed for nonnegative traveling wave solutions in a Keller--Segel chemotaxis model with logistic growth, providing precise values across relevant parameters and improving upon previous bounds.

Contribution

It establishes the exact minimum wave speed in a Keller--Segel model, extending prior bounds to precise values for all biologically relevant parameters.

Findings

Existence of a minimum wave speed for traveling waves.

Exact wave speed values are derived for all relevant parameters.

Results improve upon previous bounds by providing sharp values.

Abstract

In this paper 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 travelling 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.