Related papers: An inequality regarding non-radiative linear waves…
We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions $3 \le d \le 5$, with compactly supported initial data. In particular, it is shown that nontrivial global…
Let $\Omega$ be a vector space over a finite field with q elements. Let G denote the general linear group of endomorphisms of $\Omega$ and let us consider the left regular representation $\rho: G \to B(L_2(X))$ associated to the natural…
Using $\mathcal N=8$ supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase…
We give a survey of nonlinear potential estimates and their applications obtained recently for positive solutions to sublinear problems of the type \[ u = \mathbf{G}(\sigma u^q) + f \quad \textrm{in} \,\, \Omega, \] where $0 < q < 1$,…
The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the…
We consider a time-harmonic wave problem, appearing for example in water-waves and in acoustics, in a setting such that the analysis reduces to the study of a 2D waveguide problem with a Neumann boundary condition. The geometry is symmetric…
We study the generator $G$ of the one-dimensional damped wave equation with unbounded damping. We show that the norm of the corresponding resolvent operator, $\| (G - \lambda)^{-1} \|$, is approximately constant as $|\lambda| \to +\infty$…
This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random…
Transmission Electron Microscopy enables high-resolution imaging of materials, but the resulting images are difficult to interpret directly. One way to address this is exit wave reconstruction, i.e., the recovery of the complex-valued…
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…
We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyse linear stability of the fundamental self--similar solution of the wave equation with a focusing…
This article studies the recovery of graphons when they are convolution kernels on compact (symmetric) metric spaces. This case is of particular interest since it covers the situation where the probability of an edge depends only on some…
We generalize the energy-based discontinuous Galerkin method proposed in [SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave equations. A stability and convergence analysis is presented along with numerical…
We choose a complete set of square integrable functions as basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent wave operator is tridiagonal and…
This paper addresses several aspects of the linear Hybridizable Discontinuous Galerkin Method (HDG) for the Helmholtz equation with impedance boundary condition at high frequency. First, error estimates with explicit dependence on the wave…
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 metric towards the Euclidean metric. We also give…
In classical General Relativity, the way to exhibit the equations for the gravitational waves is based on two "tricks" allowing to transform the Einstein equations after linearizing them over the Minkowski metric. With specific notations…
In this paper, we formulate and analyse a geometric low-regularity integrator for solving the nonlinear Klein-Gordon equation in the $d$-dimensional space with $d=1,2,3$. The integrator is constructed based on the two-step trigonometric…
Using the polar decomposition of a bounded linear operator $A$ defined on a complex Hilbert space, we obtain several numerical radius inequalities of the operator $A$, which generalize and improve the earlier related ones. Among other…
Consider the energy-critical focusing wave equation in space dimension $N\geq 3$. The equation has a nonzero radial stationary solution $W$, which is unique up to scaling and sign change. It is conjectured (soliton resolution) that any…