Traveling waves for a time delayed Newtonian filtration equation

This paper deals with traveling wave solutions for a degenerate parabolic equation with time delay. We first establish the necessary and sufficient conditions to the existence of monotone nonincreasing and nondecreasing traveling wave solutions, which correspond to a unique wave speed c⁎(τ) respectively. It will be shown that the traveling wave may be a semi-finite, or infinite traveling wave under different exponents. Furthermore, we give an accurate estimation on the convergent rate for the semi-finite or infinite traveling waves.