English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article one will develop a so-called hyperboloidal foliation method,which is an energy method based on a foliation of space-time into hyperboloidalhypersurfaces. This method permits to treat the wave equations and theKlein-Gordon equations in the same framework so that one can apply it to thecoupled systems of wave and Klein-Gordon equations. As an application, one willestablish the global-in-time existence of small amplitude solution to thecoupled wave and Klei-Gordon equations with quadratic nonlinearity in fourspace-time dimensions under certain conditions. Compared with those introducedby S. Katayama, the conditions imposed in this article permit to include someimportant nonlinear terms. All of these suggests that this method may be a morenatural way of regarding the wave operator.

Global existence of small amplitude solution to nonlinear system of wave and Klein-Gordon equations in four space-time dimensions