Convergence rate in the weighted norm for a semilinear heat equation with supercritical nonlinearity

Abstract

We study the behavior of solutions to the Cauchy problem for a semilinear heat equation with supercritical nonlinearity. It is known that two solutions approach each other if these initial data are close enough near the spatial infinity. In this paper, we give its sharp convergence rate in the weighted norms for a class of initial data. Proofs are given by a comparison method based on matched asymptotics expansion.