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- Title
Global Nonlinear Stability of Traveling Wave Solution to Time-Like Extremal Hypersurface in Minkowski Space.
- Authors
Liu, Jianli; Zhou, Yi
- Abstract
There are a few results about the global nonlinear stability of nontrivial large solution to quasilinear wave equations. Time-like extremal surface in Minkowski space is an important model of quasilinear wave equation. There are two folds in this paper. Firstly, we get the existence of traveling wave solution to the time-like extremal hypersurface in |$\mathbb {R}^{1+(n+1)}$| , which can be considered as the generalized Bernstein theorem. For |$n=2$| , we are also concerned with global stability of traveling wave solutions with speed of light to time-like extremal hypersurface equation in |$1+(2+1)$| dimensional Minkowski space, which is corresponding with quasilinear wave equation in two space dimensions.
- Subjects
MINKOWSKI space; WAVE equation; PAPER arts; SPEED of light; NONLINEAR wave equations; HYPERSURFACES
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 8, p6966
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad309