Related papers: Distributed source identification for wave equatio…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
We consider the problem of pointwise estimation of multi-dimensional signals $s$, from noisy observations $(y_\tau)$ on the regular grid $\bZd$. Our focus is on the adaptive estimation in the case when the signal can be well recovered using…
We put forward a model that describes a decaying and evanescent point source of non-interacting quantum waves in 1D. This point-source assumption allows for a simple description that captures the essential aspects of the dynamics of a wave…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…
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…
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…
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope…
In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani, Tucsnak and Weiss [15]. Based on the concept of observers (also called Luenberger observers), this…
This note investigates the distributed estimation problem for continuous-time linear time-invariant (LTI) systems observed by a network of observers. Each observer in the network has access to only part of the output of the observed system,…
We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes…
This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…
This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are…
Motivated by an example from remote sensing of gas emission sources, we derive two novel change point procedures for multivariate time series where, in contrast to classical change point literature, the changes are not required to be…
This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing…
The problem of unknown input observer design is considered for coupled PDE/ODE systems subject to incremental sector bounded nonlinearities and unknown boundary inputs. Assuming available measurements at the boundary of the distributed…
Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…