Uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski space

Jianli Liu; Yi Zhou

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arXiv · 1903.04129

Uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski space

Jianli Liu·Yi Zhou

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Abstract

There is a few results about the global stability of nontrivial solutions to quasilinear wave equations. In this paper we are concerned with the uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski space. Firstly, we can get the existence and uniqueness of traveling wave solutions to the time-like extremal hypersurface in R1+(n+1), which can be considered as the generalized Bernstein theorem in Minkowski space. Furthermore, we also get the stability of traveling wave solutions with speed of light to time-like extremal hypersurface in 1 + (2 + 1) dimensional Minkowski space.

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Jianli Liu, Yi Zhou. 2019-03-11. Uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski space. https://arxiv.org/abs/1903.04129

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