Keel, Markus; Smith, Hart F.; Sogge, Christopher D. Almost global existence for some semilinear wave equations. (English) Zbl 1031.35107 J. Anal. Math. 87, 265-279 (2002). This paper is devoted to the almost global existence of solutions of three-dimensional quadrically semilinear wave equations with the use of classical invariance of the equations under translations and spatial rotation. Using these techniques, the authors can handle semilinear wave equations in Minkowski space or semilinear Dirichlet-wave equations in the exterior of a nontrapping obstacle. Reviewer: Messoud Efendiev (Berlin) Cited in 4 ReviewsCited in 70 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 58J70 Invariance and symmetry properties for PDEs on manifolds Keywords:classical invariance; Minkowski space; exterior of a nontrapping obstacle PDFBibTeX XMLCite \textit{M. Keel} et al., J. Anal. Math. 87, 265--279 (2002; Zbl 1031.35107) Full Text: DOI arXiv References: [1] P. S. Datti,Nonlinear wave equations in exterior domains, Nonlinear Anal.15 (1990), 321-331. · Zbl 0738.35043 · doi:10.1016/0362-546X(90)90140-C [2] F. John and S. Klainerman,Almost global existence to nonlinear wave equations in three dimensions Comm. Pure Appl. Math.37 (1984), 443-455. · Zbl 0599.35104 · doi:10.1002/cpa.3160370403 [3] M. Keel, H. Smith and C. D. Sogge,Global existence for a quaslinear wave equation outside of star-shaped domains, J. Funct. Anal.189 (2002), 155-226. · Zbl 1001.35087 · doi:10.1006/jfan.2001.3844 [4] S. Klainerman,Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math.38 (1985), 321-332. · Zbl 0635.35059 · doi:10.1002/cpa.3160380305 [5] S. Klainerman and T. Sideris,On almost global existence for nonrelativistic wave equations in 3d, Comm. Pure Appl. Math.49 (1996), 307-321. · Zbl 0867.35064 · doi:10.1002/(SICI)1097-0312(199603)49:3<307::AID-CPA4>3.0.CO;2-H [6] P. D. Lax, C. S. Morawetz and R. S. Phillips,Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle, Comm. Pure Appl. Math.16 (1963), 477-486. · Zbl 0161.08001 · doi:10.1002/cpa.3160160407 [7] C. S. Morawetz,The decay of solutions of the exterior initial-boundary problem for the wave equation, Comm. Pure Appl. Math.14 (1961), 561-568. · Zbl 0101.07701 · doi:10.1002/cpa.3160140327 [8] C. S. Morawetz, J. Ralston and W. Strauss,Decay of solutions of the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math.30 (1977), 447-508. · Zbl 0372.35008 · doi:10.1002/cpa.3160300405 [9] H. Smith and C. D. Sogge,Global Strichartz estimates for nontrapping perturbations of the Laplacian, Comm. Partial Differential Equations25 (2000), 2171-2183. · Zbl 0972.35014 · doi:10.1080/03605300008821581 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.