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 u t - Δ u + α (t , y) u x = f (t , y , u) 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. [ABSTRACT FROM AUTHOR]