Related papers: Localized energy for wave equations with degenerat…

We establish global well-posedness and scattering results for the logarithmically energy-supercritical nonlinear wave equation, under the assumption that the initial data satisfies a partial symmetry condition. These results generalize and…

The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…

We introduce and study a generalized energy conservation relation for scattering of time-modulated waves, where conventional energy conservation does not hold. Based on this relation, we derive an optical theorem and compute the active…

We reconsider the theory of scattering for some long range Hartree equations with potential |x|^-gamma with 1/2 < gamma < 1. More precisely we study the local Cauchy problem with infinite initial time, which is the main step in the…

An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral type featuring contributions of bulk and interfacial…

Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…

The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random…

Wave chaos is demonstrated by studying a wave propagation in a periodically corrugated wave-guide. In the limit of a short wave approximation (SWA) the underlying description is related to the chaotic ray dynamics. In this case the control…

We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly understood, this paper is mainly about the contribution of low…

This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…

We investigate the low regularity local well-posedness of two-dimensional irrotational deep hydroelastic waves. Building on the approach of Ifrim-Tataru [29] and Ai-Ifrim-Tataru [5], in particular by constructing a cubic modified energy…

This paper aims to establish the local and global well-posedness theory in $L^1$, inspired by the approach of Keel and Tao [Internat. Math. Res. Notices, 1998], for the forced wave map equation in the ``external'' formalism. In this…

A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric…

We study the low regularity well-posedness for Cauchy problem of 3D relativistic Euler equations. Firstly, we introduce a new decomposition for relativistic velocity and derive new transport equations for vorticity, which both play a…

This paper describes a general formalism for obtaining localized solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems. This class includes the important cases of Schr\"odinger's…

We are concerned with solutions to the linear wave equation. We give an asymptotic formula for large time, valid in the energy space, via an operator related to the Radon transform. This allows us to show that the energy is concentrated…

We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schr\"odinger equation with localized driving, when supplemented with vanishing boundary conditions. Their derivation…

Local entropic loss functions provide a versatile framework to define architecture-aware regularization procedures. Besides the possibility of being anisotropic in the synaptic space, the local entropic smoothening of the loss function can…

Localized states universally appear when a periodic potential is perturbed by defects or terminated at its surface. In this Letter, we theoretically and experimentally demonstrate a mechanism that generates localized states through…

- In this article, we prove some universal bounds on the speed of concentration on small (frequency-dependent) neighborhoods of submanifolds of L 2-norms of quasi modes for Laplace operators on compact manifolds. We deduce new results on…