Related papers: Homogenization of the one-dimensional wave equatio…
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains using modeling for non-periodic domains with…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling…
Three problems about recovery of a high-frequency free term in the one-dimension wave equation with homogeneous initial-boundary conditions by some information about partial asymptotics of its solution have been solved. It is shoun, that…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
The convergence of spectra via two-scale convergence for double-porosity models is well known. A crucial assumption in these works is that the stiff component of the body forms a connected set. We show that under a relaxation of this…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
This article studies the homogenization of hyperbolic-parabolic equations in porous media with tiny holes. We assume that the holes are periodically distributed and that the coefficients of the equations are periodic. Using the multi-scale…
We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\R^n$, $n \in \{1, 2, 3\}$. Standard homogenization theory provides, for the limit of a small periodicity length…
A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to model the macroscopic dynamics…
In this study, we establish an inclusive paradigm for the homogenization of scalar wave motion in periodic media (with or without the source term) at finite frequencies and wavelengths spanning the first Brioullin zone. We take the…
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
A theoretical model to explain the scattering process of wave attenuation in a marginal ice zone is developed. Many field observations offer wave energy decay in the form of exponential function with distance, and this is justified through…
Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…