Propagation Speed of Degenerate Diffusion Equations with Time Delay

We are concerned with a class of degenerate diffusion equations time delay describing population dynamics age structure. In our recent study [Nonlinearity, 33 (2020), 4013–4029], we established the existence and uniqueness critical traveling wave for time-delayed equations, obtained reducing mechanism on speed. this paper, now able to show asymptotic spreading speed its coincidence $$c^*(m,r)$$ sharp wave, prove that initial perturbation or boundary compact support solution propagates at equations. Remarkably, different from existing studies related speeds, lead some essential difficulties in analysis speed, because makes waves slow down more complicated fashion such cannot be determined by characteristic equation, causes loss regularity solutions. By phase transform technique construct upper lower solutions semi-compact supports then determine Furthermore, propose brand-new sharp-profile-based difference scheme handle large variation $$(u^m)_{xx}$$ near edge carry out numerical simulations which perfectly confirm theoretical results.