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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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