Existence results for nonlinear wave equations

In Section 2, we review spherical analysis on noncompact symmetric spaces, and recall pointwise estimates of wave kernels on rank one symmetric space obtained in [3].. In Section

While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it

Based on the well-known Mountain Pass Lemma due to Ambrosetti and Rabinowitz, we will show in Theorem 3.18 and Theorem 3.19 that if κ is suitably large, then among all nonzero

We study here instability problems of standing waves for the nonlinear Klein–Gordon equations and solitary waves for the generalized Boussinesq equations.. It is shown that

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class

Keywords: Nonlinear damped wave equation, Global existence, Blow-up, Critical exponent, Large time asymptotic behavior.. 2010 MSC: 35L15, 35L70,

The wave equation (6) was also investigated on the 3–dimensional hyperbolic space by Metcalfe and Taylor [27], who proved dispersive and Strichartz estimates with applica- tions

We first present numerical experiments for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime, then we consider a stiffer problem, the nonlinear Schr¨