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Table 1 Table summarizing our findings on the existence of travelling wave solutions (TWS)

From: Travelling wave analysis in chemotaxis: case of starvation

h(S)

k

\(D_{S}\)

TWS

Restriction on \(\alpha _{0}\)

0

\(\infty \)

0

\(\times \) (or \(\surd \) if \(S_{1} \notin Y_{S}\))

\(\ne 0\)

\(\times \) (or \(\surd \) if \(S_{1} \notin Y_{S}\))

0

0

\(\times \)

\(\ne 0\)

\(\surd \)

\(\alpha _{0}\)

\(\infty \)

0

\(\times \) (or \(\surd \) if \(S_{1} \notin Y_{S}\))

– (or arbitrary)

\(\ne 0\)

\(\surd \)

\(\alpha _{0}>2 \lambda _{0}\)

0

0

\(\times \)

\(\ne 0\)

\(\surd \)

\(\alpha _{0}\le 2 \lambda _{0}\)