Asymptotics for a nonlinear integral equation with a generalized heat kernel

Abstract

This paper is concerned with a nonlinear integral equation(Formula presented.)where(Formula presented.) for some K ≥ 0. Here, G = G(x,t) is a generalization of the heat kernel. We are interested in the asymptotic expansions of the solution of (P) behaving like a multiple of the integral kernel G as t→∞.