arXiv Analytics

Sign in

arXiv:1101.3657 [math.AP]AbstractReferencesReviewsResources

Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions

Soichiro Katayama

Published 2011-01-19, updated 2012-06-04Version 2

In connection with the weak null condition, Alinhac introduced a sufficient condition for global existence of small amplitude solutions to systems of semilinear wave equations in three space dimensions. We introduce a slightly weaker sufficient condition for the small data global existence, and we investigate the asymptotic pointwise behavior of global solutions for systems satisfying this condition. As an application, the asymptotic behavior of global solutions under the Alinhac condition is also derived.

Comments: 56 pages, the final version
Journal: Journal of Hyperbolic Differential Equations, Vol.9, Issue 2 (2012), 263-323
Categories: math.AP
Subjects: 35L70
Related articles: Most relevant | Search more
arXiv:1111.4231 [math.AP] (Published 2011-11-17)
The energy decay and asymptotics for a class of semilinear wave equations in two space dimensions
arXiv:1208.3531 [math.AP] (Published 2012-08-17)
Almost global existence for exterior Neumann problems of semilinear wave equations in 2D
arXiv:1309.6006 [math.AP] (Published 2013-09-23, updated 2014-06-06)
Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions

Links

Toolbox