Existence globale et comportement asymptotique pour l’équation de Klein-Gordon quasi linéaire à données petites en dimension $1$

@inproceedings{Delort2001ExistenceGE,
  title={Existence globale et comportement asymptotique pour l’{\'e}quation de Klein-Gordon quasi lin{\'e}aire {\`a} donn{\'e}es petites en dimension \$1\$},
  author={J Delort},
  year={2001}
}
Let v be a solution to a quasilinear Klein–Gordon equation in one space dimension □v+v=F(v,∂tv,∂xv,∂t∂xv,∂x2v) with smooth compactly supported Cauchy data of size e→0. Assume that F vanishes at least at order 2 at 0. It is known that the solution v exists over an interval of time of length larger than ec/e2 for a positive c, and that for a general F it blows up in finite time ec′/e2 (c′>0). We conjectured in [7] a necessary and sufficient condition on F under which the solution should exist… CONTINUE READING

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