We study the lifespan of solutions to fully nonlinear second-order Cauchy problems with small real- or complex-analytic data. The nonlinear term is an analytic function in u, ū and their derivatives. We give an outline of the proof based on the method of majorants and the fixed point technique.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-11,
author = {Hideshi Yamane},
title = {Nonlinear Cauchy problems with small analytic data and the lifespan of their solutions},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {153-160},
zbl = {1262.35147},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-11}
}
Hideshi Yamane. Nonlinear Cauchy problems with small analytic data and the lifespan of their solutions. Banach Center Publications, Tome 97 (2012) pp. 153-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-11/