Dynamical behavior near explicit self-similar blow up solutions for the Born-Infeld equation

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 are given inside a strictly proper subset of the backward light cone.

arXiv comment31 pages

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Cited by in corpus (4)

• Thermal fluctuations of (non)linearly charged BTZ black hole in massive gravity
• Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons
• Global stability dynamics of the timelike extremal hypersurfaces in Minkowski space
• Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in R^{1+3}