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In this talk I plan to survey some progress on Hardy and BMO spaces, Riesz transforms, Bochner-Riesz means and spherical means by using the method of wave equation,and show interesting connections and...
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
We introduce a new multiscale Gaussian beam method for the numerical solution of the wave equation with smooth variable coefficients. The first computational question addressed in this paper is how to...
The Gaussian beam method is an asymptotic method for wave equations with highly oscillatory data. In a recent published paper by two of the authors, a multiscale Gaussian beam method was first propose...
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-...
High-resolution 3-D P and S wave crustal velocity and Poisson's ratio models of the 1992 Landers earthquake (Mw 7.3) area are determined iteratively by a wave-equation-based travel-time seismic tomogr...
In this paper, we propose a wave-equation-based travel-time seismic tomography method with a detailed description of its step-by-step process. First, a linear relationship between the travel-time resi...
We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' principle. A similar an...
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on an arbitrarily shaped bounded domain $\Omega \subset \R^2$. As a main result we ...
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the weight of the delay ter...
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering f...
In this paper, we describe the asymptotic behaviour of globally defined solutions and of bounded solutions blowing up in finite time of the radial energy-critical focusing non-linear wave equation in ...
Abstract: We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the ...
Abstract: In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local e...
Abstract: In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equa...

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