2 citations · 3 across the 4 of their papers we have counts for
16 papers
Nonlinear hyperbolic equations in infinite homogeneous waveguides
Jason Metcalfe, Christopher D. Sogge, Ann Stewart
In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both…
Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains
Jason Metcalfe, Makoto Nakamura, Christopher D. Sogge
In this paper we prove global existence for certain multispeed Dirichlet-wave equations with quadratic nonlinearities outside of obstacles. We assume the natural null condition for…
Global existence for Dirichlet-wave equations with quadratic nonlinearties in high dimensions
Jason Metcalfe, Christopher D. Sogge
We prove global existence of solutions to quasilinear wave equations with quadratic nonlinearities exterior to nontrapping obstacles in spatial dimensions four and higher. This gen…
Estimates for the Dirichlet-wave equation and applications to nonlinear wave equations
Christopher D. Sogge
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions ou…
Eigenfunction and Bochner Riesz estimates on manifolds with boundary
Christopher D. Sogge
The purpose of this paper is to give a simple proof of sharp estimates for the eigenfunctions of the Dirichlet Laplacian on smooth compact Riemannian manifolds o…
Global existence for nonlinear wave equations with multiple speeds
Christopher D. Sogge
We shall be concerned with the Cauchy problem for quasilinear systems in three space dimensions of the form \label{i.1} \partial^2_tu^I-c^2_IΔu^I = C^{IJK}_{abc}\partial_c u^J\part…