We consider the behavior of solutions to the Cauchy problem for a semilinear heat equation with supercritical nonlinearity. We study the convergence of solutions to steady states in a weighted norm, and show the global attractivity property of steady states. We also give its convergence rate for a class of initial data. Proofs are given by a comparison method based on matched asymptotic expansion.
"Global attractivity and convergence rate in the weighted norm for a supercritical semilinear heat equation." Differential Integral Equations 28 (7/8) 777 - 800, July/August 2015.