Related papers: Inverse Problems for Hyperbolic Equations
This paper deals with left invertibility problem of implicit hyperbolic systems with delays in infinite dimensional Hilbert spaces. From a decomposition procedure, invertibility for this class of systems is shown to be equivalent to the…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a…
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an…
In this paper, we consider an inverse problem for three dimensional viscoelastic fluid flow equations, which arises from the motion of Kelvin-Voigt fluids in bounded domains (a hyperbolic type problem). This inverse problem aims to…
We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics.…
We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…
We consider the Cauchy problem for strictly hyperbolic $m$-th order partial differential equations with coefficients low-regular in time and smooth in space. It is well-known that the problem is $L^2$ well-posed in the case of Lipschitz…
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…
In this paper, we investigate the initial value problem for symmetric hyperbolic systems on globally hyperbolic Lorentzian manifolds with potentials that are both nonlocal in time and space. When the potential is retarded and uniformly…
This is the third part of a four-paper sequence, which establishes the Threshold Conjecture and the Soliton-Bubbling vs.~Scattering Dichotomy for the energy critical hyperbolic Yang--Mills equation in the $(4+1)$-dimensional Minkowski…
In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension $n\geq 2$. In particular we consider the so called interior determination problem. This non-linear wave…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
We consider the inverse problem of determining a compact Riemannian manifold with boundary from fixed time observations of the solution, restricted to a small subset in space, for the Navier-Stokes system with a local source on the…
In this article, we consider linear hyperbolic Initial and Boundary Value Problems (IBVP) in a rectangle (or possibly curvilinear polygonal domains) in both the constant and variable coefficients cases. We use semigroup method instead of…
In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the…