We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am38-4-3,
author = {Jianwei Yang},
title = {Global existence for nonlinear system of wave equations in 3-D domains},
journal = {Applicationes Mathematicae},
volume = {38},
year = {2011},
pages = {435-452},
zbl = {1231.35114},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-4-3}
}
Jianwei Yang. Global existence for nonlinear system of wave equations in 3-D domains. Applicationes Mathematicae, Tome 38 (2011) pp. 435-452. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-4-3/