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

Laboratoire de Mathématiques d’Orsay (LMO), Université Paris-Saclay, Bâtiment 307, rue Michel, Magat, F-91405 Orsay Cedex, France

E-mail Address: philippe.anjolras@universite-paris-saclay.fr

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https://doi.org/10.1142/S0219891624500139Cited by:0 (Source: Crossref)

Abstract

In this paper, we consider the Born–Infeld system, arising as a nonlinear model of electromagnetism, and its extension introduced by Brenier [Hydrodynamic structure of the augmented Born–Infeld equations, Arch. Ration. Mech. Anal. 172(1) (2004) 65–91] the so-called “augmented Born–Infeld system”. We show that this system enjoys a non-resonance structure and prove global existence and linear asymptotic behavior of small (admissible) perturbations of arbitrary constant states.

Communicated by P. Germain

Keywords:

AMSC: 35B40, 35A01, 35Q60, 78A25

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