Related papers: An inverse problem for the time-dependent linear B…
In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension $n \geq 3$. The stability estimates correspond to a couple of uniqueness results by Dos Santos…
The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.…
In this work, we explore various relevant aspects of the Smoothed Particle Hydrodynamics regarding Burger's equation. The stability, precision, and efficiency of the algorithm are investigated in terms of different implementations. In…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
We consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…
This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…
In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…
The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…
The inelastic Boltzmann equation for a granular gas is applied to spatially inhomogeneous states close to the uniform shear flow. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution. The…
We perform the analysis of the focusing nonlinear Schr\"odinger equation on the half-line with time-dependent boundary conditions along the lines of the nonlinear method of images with the help of B\"acklund transformations. The difficulty…
This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…
We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
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 demonstrate that simultaneous reconstruction of scattering and absorption of a mesoscopic system using angularly-resolved measurements of scattered light intensity is possible. Image reconstruction is realized based on the algebraic…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
We study analytically the dynamics of an anisotropic particle subjected to different stochastic resetting schemes in two dimensions. The Brownian motion of shape-asymmetric particles in two dimensions results in anisotropic diffusion at…
In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from…
The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle distribution functions (PDFs). Despite its success, solving…
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption…