arXiv subjects

Antônio Marcos da Silva

Publications and source records attributed to Antônio Marcos da Silva.

3 recordsLinked to original sources

arXiv2025

The Diffusive Behavior of Solutions to the Linear Damped Wave Equation: an Undergraduate D.I.Y. Classnote

Despite of the fact that the Damped Wave and the Heat equations describe phenomena of distinct nature, it is amazing that their solutions are related in the limit as $t \to \infty$. The aim of this note is to explain to undergraduate students, with a good calculus background, how the relation between these solutions is established. We follow a ``do it yourself'' strategy and the students are invited to do the suggested exercises in order to understand the content of this note.

math.HO↗

arXiv2025

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

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}.

math-ph↗

arXiv2022

Higher Order Asymptotics of Decaying Solutions of some Generalized Burgers Equations

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.

math-ph↗