ABSTRACT In this paper, we develop new ideas to establish the existence of traveling waves to a precursor and differentiated cell model with degenerate nonlinearity and non‐isolated equilibria. Our new approach is based on continuation argument and the abstract implicit function theorem coupled with the upper–lower solution method, which seems to be able to widely apply to many other systems with degenerate nonlinearity and/or non‐isolated equilibria. We prove that the traveling wave with the minimal speed decays exponentially to zero at positive infinity, while for all other speeds, the decay is algebraic. Furthermore, due to the significance of the minimal speed (usually regarded as the spreading speed), we provide an estimate of it. In particular, when the parameter , we derive an exact value of the minimal wave speed and the expression of the traveling wave solution with the minimal‐speed.
Yue et al. (Mon,) studied this question.