On the Global Solutions of Abstract Wave Equations with High Energies
-
Published:2022-04
Issue:3-4
Volume:111
Page:525-533
-
ISSN:0001-4346
-
Container-title:Mathematical Notes
-
language:en
-
Short-container-title:Math Notes
Author:
Esquivel-Avila J. A.
Publisher
Pleiades Publishing Ltd
Subject
General Mathematics
Reference26 articles.
1. M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and Applications (Birkhäuser, Boston, 1996), Vol. 24.
2. L. E. Payne and D. H. Sattinger, “Saddle points and instability of nonlinear hyperbolic equations,” Israel J. Math. 22, 273–303 (1975).
3. F. Gazzola and M. Squassina, “Global solutions and finite time blow up for damped semilinear wave equations,” Ann. Inst. H. Poincaré Anal. Non Linéaire 23, 185–207 (2006).
4. Y. Wang, “A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrarily positive initial energy,” Proc. Amer. Math. Soc. 136, 3477–3482 (2008).
5. H. A. Levine and G. Todorova, “Blow up of solutions of the Cauchy problem for a wave equation with nonlinear damping and source terms and positive initial energy,” Proc. Amer. Math. Soc. 129, 793–805 (2001).