The asymptotic stability of diverging traveling waves for reaction-advection-diffusion equations in cylinders

This paper is devoted to the asymptotic stability of diverging traveling waves for reaction-advection-diffusion equation ut-Delta u+alpha(t,y)ux=f(t,y,u)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{t}-\Delta u+\alpha (t,y)u_{x}=f(t,y,u)$$\end{document} in cylinders. By the sliding method, we first establish a Liouville-type result. Then, using the Liouville-type result and truncation technique, we prove the asymptotic stability of the diverging traveling wave.