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This paper deals with the existence of traveling waves for doubly nonlinear degenerate diffusion equations with Nicholson's blowflies-type source term and time delay. We prove the existence of monotone and non-monotone traveling waves by the monotone iteration and Schauder's fixed point theorem respectively. Furthermore, the non-critical traveling waves are proven to be globally-stable. The adopted approach for the proof is the weighted energy method combining the compactness analysis.

Smooth traveling waves for doubly nonlinear degenerate diffusion equations with time delay