Almost global existence for some semilinear wave equations

2001/08/02 by Markus Keel, M. Keel, Hart Smith +5 · 3 citations
Engineering · Mathematics · #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Stability and Controllability of Differential Equations #math.AP #msc:35L70

paper · pdf · doi:10.48550/arxiv.math/0108016

To appear in Journal d'Analyse. A paper on the quasilinear case will follow

arxiv created 2001/08/02 · openalex publication_date 2001/08/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave equations, as opposed to the much harder to prove 1/t decay.

Citations

• On almost global existence for nonrelativistic wave equations in 3D
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Global Strichartz estimates for nontrapping perturbations of the Laplacian

Cited by

• Logarithmic wave decay for short range wavespeed perturbations with radial regularity
• Global smooth solutions of 2-D quadratically quasilinear wave equations with null conditions in exterior domains, II
• Long-Time Existence of Quasilinear Wave Equations Exterior to Star-shaped Obstacle in 2D

Related

• Global existence for semilinear wave equations exterior to nontrapping obstacles
• Almost global existence for exterior Neumann problems of semilinear wave equations in 2D
• Almost global existence for quasilinear wave equations in three space dimensions
• Almost Global Existence for 4-Dimensional Quasilinear Wave Equations in Exterior Domains
• Global existence for systems of quasilinear wave equations in (1+4)-dimensions