Related papers: Low frequency dispersive estimates for the wave eq…
In this papwe we consider an effective role of the potential of the wave equations with/without damping on the L^{2}-estimate of the solution itself. In the free wave equation case it is known that the L^{2}-norm of the solution itself…
We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in $n+1$ dimensions for odd $n$ and obtain improved estimates in even dimensions. This is achieved by deriving local smoothing estimates for certain…
We formulate the Born approximation for finding resonance poles in the complex plane for potential scattering problems. Using the method, we study the distribution of resonance poles for several scattering potentials. In particular, we find…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…
We examine the response of a plane wave incident on a flat surface of a medium characterized by simultaneously negative electric and magnetic susceptibilities by solving Maxwell's equations explicitly and without making any assumptions on…
This paper introduces a high-dimensional linear IV regression for the data sampled at mixed frequencies. We show that the high-dimensional slope parameter of a high-frequency covariate can be identified and accurately estimated leveraging…
We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The…
High accuracy calculations of atomic properties require using long basis sets. In particular, it is necessary to include large number of partial waves and estimate truncation corrections. The convergence in partial waves is known to be…
We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation.…
We construct a new compact semi-explicit three-level in time fourth-order finite-difference scheme for numerical solving the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are…
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range…
Within a Liouville approach to non-critical string theory, we discuss space-time foam effects on the propagation of low-energy particles. We find an induced frequency-dependent dispersion in the propagation of a wave packet, and observe…
We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering…
This paper can be considered as a sequel of [BS14] by Bernicot and Samoyeau, where the authors have proposed a general way of deriving Strichartz estimates for the Schr{\"o}dinger equation from a dispersive property of the wave propagator.…
We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
The problem of estimating the frequencies of an exponential sum has been studied extensively over the last years. It can be understood as a sparse estimation problem, as it strives to identify the sparse representation of a signal using…
We present a linear mode analysis of the relativistic MHD equations in the presence of finite electrical conductivity. Starting from the fully relativistic covariant formulation, we derive the dispersion relation in the limit of small…
This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…