A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations

Abstract

In this paper, we consider the asymptotic behavior of traveling wave solutions of a certain degenerate nonlinear parabolic equation for $\xi \equiv x - ct \to - \infty$ with $c>0$. We give a refined one of them, which was not obtained in the preceding work [Ichida-Sakamoto, J. Elliptic and Parabolic Equations, to appear], by an appropriate asymptotic study and properties of the Lambert $W$ function.