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Three-dimensional central symmetric bodies different from spheres that can float in all orientations are considered. For relative density rho=1/2 there are solutions, if holes in the body are allowed. For rho different from 1/2 the body is…
We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…
We describe a simple experimental apparatus which allows one to observe the wave properties of light in a new way. This apparatus also makes possible to introduce and illustrate, in a very suggestive way, some fundamental principles of…
An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three-…
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with…
In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For…
In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave…
A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of…
A 3+1 spacetime, with a shift vector that is the unique fundamental solution to the linearized wave operator, is introduced to model an interpretation of Wheeler's layman's analogy of the Quantum foam. To understand the distributional…
We study the symmetry reduction of nonlinear evolution and wave type differential equations by using operators of non-point symmetry. In our approach we use both operators of classical and conditional symmetry. It appears that the…
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…
We generalize our previous linear result [1] in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly…
The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a…
We prove global well-posedness for the defocusing cubic wave equation with data in $H^{s} \times H^{s-1}$, $1>s>{13/18}$. The main task is to estimate the variation of an almost conserved quantity on an arbitrary long time interval. We…
We prove the local energy decay for the wave equation in a wave guide with dissipation at the boundary. It appears that for large times the dissipated wave behaves like a solution of a heat equation in the unbounded directions. The proof is…
Solutions to the wave equation with constant coefficients in $\mathbb{R}^d$ can be represented explicitly in Fourier space. We investigate a reconstruction formula, which provides an approximation of solutions $u(.,t)$ to initial data…
We study the decay rate for the energy of solutions of a damped wave equation in a situation where the Geometric Control Condition is violated. We assume that the set of undamped trajectories is a flat torus of positive codimension and that…
We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We establish inversion formulas of the so called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several…