To substantiate the asymptotics of solving the Cauchy problem for a singularly perturbed weakly nonlinear transport equation

TL;DR

This paper proves a theorem providing uniform estimates for the residual of asymptotic expansions in solving a singularly perturbed weakly nonlinear transport equation, addressing the critical case in the Cauchy problem.

Contribution

It introduces a rigorous theorem for uniform residual estimation in asymptotic solutions of singularly perturbed nonlinear transport equations.

Findings

Established uniform residual bounds for asymptotic solutions

Addressed the critical case in singular perturbation analysis

Enhanced understanding of solution behavior in weakly nonlinear transport equations

Abstract

A theorem is proved on the uniform estimation of the residual term of the asymptotic expansion with respect to a small parameter of the solution of the initial problem for a singularly perturbed differential operator weakly nonlinear transport equation in the critical case.