期刊
NONLINEARITY
卷 32, 期 12, 页码 4682-4712出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/ab34a2
关键词
blow-up solution; stability; Born-Infeld equation
资金
- NSFC [11771359]
- Fundamental Research Funds for the Central Universities [20720190070, 201709000061, 20720180009]
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.
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