Higher Order Asymptotics of Decaying Solutions of some Generalized Burgers Equations

TL;DR

This paper develops a modified Renormalization Group approach to analyze the higher order asymptotic behavior of solutions to generalized Burgers equations with zero mass initial data, enhancing understanding of their long-term dynamics.

Contribution

It introduces a novel modification of the Renormalization Group map to obtain higher order asymptotics for nonlinear time-evolution equations like the generalized Burgers equation.

Findings

Derived higher order asymptotic expansions of solutions

Demonstrated the effectiveness of the modified RG map

Provided insights into the long-time behavior of solutions

Abstract

We study the large-time behavior of solutions to a generalized Burgers Equation, with initial zero mass data. Our main purpose is to present a modified version of the Renormalization Group map, which is able to provide the higher order asymptotic properties of the solution to the Cauchy problem of a class of nonlinear time-evolution problems.