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In this paper we employ the Renormalization Group (RG) method to study thelong-time asymptotics of a class of nonlinear integral equations with ageneralized heat kernel and with time-dependent coefficients. Thenonlinearities are classified and studied according to its role in theasymptotic behavior. Here we prove that adding nonlinear perturbationsclassified as irrelevant, the behavior of the solution in the limit $t\to\infty$ remains unchanged from the linear case. In a companion paper, wewill include a type of nonlinearities called marginal and we will show that, inthis case, the large time limit gains an extra logarithmic decay factor.

Asymptotics for Nonlinear Integral Equations with Generalized Heat Kernel and Time Dependent Coefficients Using Renormalization Group Technique