Dynamical behavior near explicit self-similar blow–up solutions for the Born–Infeld equation. (21st October 2019)

• Record Type: Journal Article
• Authors: Yan, Weiping
• Is Part Of: Nonlinearity. Volume 32:Number 12(2019)
• Page Start: 4682
• Page End: 4712
• Publication Date: 2019-10-21
• Subjects: blow-up solution -- stability -- Born–Infeld equation; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab34a2
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: This paper studies the dynamical behavior near a new family of explicit self-similar solutions for the one-dimensional Born–Infeld equation. This quasilinear scalar field equation arises from nonlinear electromagnetism, as well as branes in string theory and minimal surfaces in Minkowski spacetimes. We show that both this model and the linear wave equation admit the same family of explicit timelike self-similar blow-up solutions; meanwhile, Lyapunov nonlinear stability of those self-similar blow-up solutions is given inside a strictly proper subset of the backward light cone.