Abstract
Lagrangian mean curvature flow has been studied extensively recently and many important results have been obtained. In this paper, we attempt to consider the hyperbolic version of Lagrangian mean curvature flow, which is a nonlinear wave equation for the potential function u(x) of a graph submanifold (x,Du(x)) in R2n. In particular, here we are interested in the one dimensional case. Assume the initial data are periodic and under some suitable conditions, we are able to show that the C3 solution to the above hyperbolic mean curvature flow for Lagrangian graphs must blow up in finite time and the lifespan can be also derived.
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