Variational Approach of Critical Sharp Front Speeds in Density-dependent Diffusion Model with Time Delay.

For the classical reaction diffusion equation, the priori speed of fronts is determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier, {\em Commun. Math. Phys.} 175:221--227, 1996) by variational characterization method. In this paper, we model the dispersal process using a density-dependent diffusion equation with time delay. We show the existence and uniqueness of sharp critical fronts, where the sharp critical front is $C^1$-smooth when the diffusion degeneracy is weaker with $1

Keywords:

• Mathematics
• Piecewise
• Mathematical analysis
• Reaction–diffusion system
• Diffusion equation
• Degeneracy (mathematics)
• Diffusion (business)
• Uniqueness
• density dependent
• traveling wave

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