The goal of this article is to establish general principles for high frequency dispersive
estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We construct …

We consider the defocusing, cubic nonlinear wave equation with zero Dirichlet boundary
value in the exterior $\Omega=\R^ 3\backslash\bar {B}(0, 1) $. We make use of the distorted …

We continue the study of the Dirichlet boundary value problem of nonlinear wave equation
with radial data in the exterior $\Omega=\mathbb {R}^ 3\backslash\bar {B}(0, 1) $. We …

We prove that solutions to the quintic semilinear wave equation with variable coefficients in
R 1+ 3 scatter to a solution to the corresponding linear wave equation. The coefficients are …

{(∂ 2 t−∆) u (t, x)= F (u),(t, x)∈ R× R3 (u,∂ tu)| t= 0=(u0, u1), u\∂ Ω= 0, where the initial data
(u0, u1) is assumed to be in a Sobolev space, and in particular to have some decay at …

We investigate the asymptotic behaviour of solutions to a range of linear and nonlinear
hyperbolic equations on asymptotically flat spacetimes. We develop a comprehensive …