Asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique

Abstract

In this paper, we employ the renormalization group method to study the long-time asymptotics of solutions to a class of nonlinear integral equations with a generalized heat kernel. The nonlinearities are classified and studied according to its role in the asymptotic behavior. Here we prove that the behavior, in the limit as t goes to infinity, remains unchanged when compared with the one in the linear case if the nonlinearities are the ones classified as irrelevant in the renormalization group sense.