Traveling wavefronts for a time delayed non-Newtonian filtration equation

This paper is concerned with traveling wavefronts for the evolutionary p -Laplacian with time delay. We first establish some necessary and sufficient conditions for the existence of monotone nondecreasing and nonincreasing traveling wavefronts, which correspond to definite wave speeds c 1 ∗ and c 2 ∗ respectively. Moreover, special attention is also paid to the asymptotic behavior of traveling fronts connecting two uniform steady states.