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 \(u_{t}-\Delta u+\alpha (t,y)u_{x}=f(t,y,u)\) $u_t-\mathrm{\Delta }u+\alpha (t,y)u_x=f(t,y,u)$ 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.