Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity

This paper establishes the nonlinear stability of traveling wave solutions to a chemotaxis model with singular (or logarithmic) sensitivity and its transformed parabolic-hyperbolic system. Depending on the parameter signs, we discuss the linear instability of traveling wave solutions using the spectral analysis and nonlinear asymptotic stability of traveling wave solutions with zero end state by the weighted energy estimates, where the latter result solves the open question left in a previous work (Li and Wang, 2009 [7]).