摘要：In this talk, we present our new results on stability of oscillatory
traveling waves for a class of reaction-diffusion equations with
time-delay. The typical model is the Nicholson’s blowflies equation. When the birth rate function is non-monotone, the equation losses its
monotonicity, and the traveling waves are oscillating for a large
time-delay. These cause the study totally different from the monotone case, and will be more challenging. By using the technical weighted energy method with some new development, and the Halanay’s inequality, we prove that, for all non-critical monotone/non-monotone traveling waves, they are time-exponentially stable, and for all critical monotone/non-monotone traveling waves, they are time-algebraically stable. Some numerical computations will be also reported, which further confirm and support our theoretical results. This is a joint work with Xiongfeng Yang and Qifeng Zhang.