Related papers: Distributed source identification for wave equatio…
In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is…
In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…
In this paper, we examine a discrete dynamical system defined by x(n+1) = Ax(n)+ w(n), where x takes values in a Hilbert space H and w is a periodic source with values in a fixed closed subspace W of H. Our goal is to identify conditions on…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
We numerically investigate the sensitivity of the scattered wave field to perturbations in the shape of a scattering body illuminated by an incident plane wave. This study is motivated by recent work on the inverse problem of reconstructing…
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…
In this note, we exhibit a three dimensional structure that permits to guide waves. This structure is obtained by a geometrical perturbation of a 3D periodic domain that consists of a three dimensional grating of equi-spaced thin pipes…
We study an inverse source problem for the acoustic wave equation in a random waveguide. The goal is to estimate the source of waves from measurements of the acoustic pressure at a remote array of sensors. The waveguide effect is due to…
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
The shallow water equations (SWE) are a widely used model for the propagation of surface waves on the oceans. We consider the problem of optimally determining the initial conditions for the one-dimensional SWE in an unbounded domain from a…
We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The…
Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales…
For the wave and the Schr\"odinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.
This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…
A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on…
This paper studies distributed adaptive estimation over sensor networks with partially unknown source dynamics. We present parallel continuous-time and discrete-time designs in which each node runs a local adaptive observer and exchanges…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
This paper introduces a novel recursive distributed estimation algorithm aimed at synthesizing input and state interval observers for nonlinear bounded-error discrete-time multi-agent systems. The considered systems have sensors and…