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

TL;DR

This paper refines the understanding of the asymptotic behavior of traveling wave solutions for a class of degenerate nonlinear parabolic equations, using asymptotic analysis and Lambert W function properties.

Contribution

It provides a more precise asymptotic description of traveling wave solutions, improving upon previous results by incorporating Lambert W function analysis.

Findings

Refined asymptotic behavior characterization

Use of Lambert W function in analysis

Extension of previous asymptotic results

Abstract

In this paper, we consider the asymptotic behavior of traveling wave solutions of the degenerate nonlinear parabolic equation: $u_{t}=u^{p}(u_{xx}+u)-\delta u$ ($\delta = 0$ or $1$) for $\xi \equiv x - ct \to - \infty$ with $c>0$. We give a refined one of them, which was not obtain in the preceding work [Ichida-Sakamoto, 2020], by an appropriate asymptotic study and properties of the Lambert $W$ function.