Variational approach of critical sharp front speeds in degenerate diffusion model with time delay

摘要

For the classical reaction diffusion equation, thea priorispeed of fronts is determined exactly in the pioneering paper (Benguria and Depassier 1996Commun. Math. Phys.175221-227) by variational characterization method. In this paper, we study the age-structured population dynamics using a degenerate diffusion equation with time delay. We show the existence and uniqueness of sharp critical fronts, where the sharp critical front isC(1)-smooth when the diffusion degeneracy is weaker with 1 <m< 2, and the sharp critical front is non-C-1-smooth (piecewise smooth) when the diffusion degeneracy is stronger withm > 2, and the non-critical waves areC(2)-smooth. We give a new variational approach for the critical wave speed and investigate how the time delay affects the propagation mechanism of fronts. It is shown that the time delay slows down the critical wave speed.

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