2011/07/19 by Yue Ma, MA, Yue
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1107.3679
openalex publication_date 2011/07/19 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
In this article one will develop a so-called hyperboloidal foliation method,\nwhich is an energy method based on a foliation of space-time into hyperboloidal\nhypersurfaces. This method permits to treat the wave equations and the\nKlein-Gordon equations in the same framework so that one can apply it to the\ncoupled systems of wave and Klein-Gordon equations. As an application, one will\nestablish the global-in-time existence of small amplitude solution to the\ncoupled wave and Klei-Gordon equations with quadratic nonlinearity in four\nspace-time dimensions under certain conditions. Compared with those introduced\nby S. Katayama, the conditions imposed in this article permit to include some\nimportant nonlinear terms. All of these suggests that this method may be a more\nnatural way of regarding the wave operator.\n