A Renormalization Group Approach to Higher Order Corrections to the Decay of Solutions to Nonlinear Integral Equations

TL;DR

This paper applies the Renormalization Group method to analyze higher order asymptotic corrections for nonlinear integral equations with time-dependent coefficients, extending previous work in the field.

Contribution

It introduces a RG-based approach to compute higher order asymptotics for nonlinear integral equations with generalized heat kernels.

Findings

Higher order corrections are characterized using RG techniques.

The method extends previous asymptotic analysis to more complex equations.

Results provide refined long-time behavior predictions.

Abstract

In this paper we employ the Renormalization Group (RG) method to study higher order corrections to the long-time asymptotics of a class of nonlinear integral equations with a generalized heat kernel and with time-dependent coefficients. This is a follow up of the papers \cite{bib:souz-brag-more-art,bib:souz-brag-more-marginal,bib:brag-more-silv}.