Stability of the constant states in the augmented Born-Infeld system

TL;DR

This paper proves the global stability and linear asymptotic behavior of small perturbations around constant states in the augmented Born-Infeld system, a nonlinear electromagnetism model.

Contribution

It establishes the non-resonance structure and global stability results for the augmented Born-Infeld system, extending previous models.

Findings

Global existence of small perturbations

Linear asymptotic behavior established

Non-resonance structure identified

Abstract

In this paper, we consider the Born-Infeld system, arising as a nonlinear model of electromagnetism, and its extension introduced by Brenier [Bre04] the so-called "augmented Born-Infeld system". We show that this system enjoys a non-resonance structure and prove global existence and linear asymptotic behaviour of small (admissible) perturbations of arbitrary constant states.