Related papers: Abstract wave equations with acoustic boundary con…
We review the motivations for the search of stochastic backgrounds of gravitational waves and we compare the experimental sensitivities that can be reached in the near future with the existing bounds and with the theoretical predictions.
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
This work describes and analyzes the domain derivative for a time-dependent acoustic scattering problem. We study the nonlinear operator that maps a sound-soft scattering object to the solution of the time-dependent wave equation evaluated…
The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a $C^1$ bounded domain, subject to a large external potential $\Phi(x)$…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic…
In this work we establish some new estimates for layer potentials of the acoustic wave equation in the time domain, and for their associated retarded integral operators. These estimates are proven using time-domain estimates based on theory…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…
We present a short and elegant proof of an estimate for the pressure in terms of the velocity and external data in bounded domains under the slip and Navier boundary conditions. We also show an application of this result for conditional…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
We study boundary effects in a linear wave equation with Dirichlet type conditions in a weakly curved pipe. The coordinates in our pipe are prescribed by a given small curvature with finite range, while the pipe's cross section being…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…
A new scheme is proposed for dealing with the problem of singularities in General Relativity. The proposal is, however, much more general than this. It can be used to deal with manifolds of any dimension which are endowed with nothing more…
In this paper we are interested in the mathematical and numerical analysis of the time-dependent Galbrun equa- tion in a rigid duct. This equation models the acoustic propagation in presence of flow [1]. We propose a regu- larized…
We consider the problem of reconstructing the sound field in a room using prior information of the boundary geometry, represented as a point cloud. In general, when no boundary information is available, an accurate sound field…
This paper is concerned with the analysis of the time domain acoustic scattering from two-dimensional open cavities. A transparent boundary condition is developed to reformulate the scattering problem into an equivalent initial boundary…
In the first part of this paper, we show that the Cauchy problem for wave propagation in some static spacetimes presenting a singular time-like boundary is well posed, if we only demand the waves to have finite energy, although no boundary…