Related papers: Localization of moving sources: uniqueness, stabil…
We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the…
This paper presents a method to solve the modal form of the linearised one-way Navier-Stokes (OWNS) equations for investigating disturbance development in developing subsonic and supersonic boundary layers. The modal framework offers…
We present a method of reliably extracting the flux of individual sources from sky maps in the presence of noise and a source population in which number counts are a steeply falling function of flux. The method is an extension of a standard…
We consider filters for the detection and extraction of compact sources on a background. We make a one-dimensional treatment (though a generalization to two or more dimensions is possible) assuming that the sources have a Gaussian profile…
In this contribution, we consider the problem of blind source separation in a Bayesian estimation framework. The wavelet representation allows us to assign an adequate prior distribution to the wavelet coefficients of the sources. MCMC…
Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…
We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…
Model misspecification constitutes a major obstacle to reliable inference in many inverse problems. Inverse problems in seismology, for example, are particularly affected by misspecification of wave propagation velocities. In this paper, we…
The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
The use of mobile robotics in radioactive source seeking has become an important part of modern radiation-safety practices, supporting timely mitigation of contamination risks and helping protect public health. However, measuring radiation…
In this article, we consider the inverse problems of determining the damping coefficient appearing in the wave equation. We prove the unique determination of the coefficient from the data coming from a single coincident source-receiver…
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
We study the stability/instability of the subsonic travelling waves of the Nonlinear Schr\"odinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the Grillakis-Shatah-Strauss theory, proof…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by…
It is considered the problem of localization on the plane of two radioactive sources by K detectors. Each detector records a realization of inhomogeneous Poisson process and the intensity function of this process is a sum of a signal…
We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is…
This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives…