Related papers: An Inverse Problem for the Relativistic Boltzmann …
A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.
We extend the recent study of inverse problems for minimal surfaces by considering the inverse source problem for the prescribed mean curvature equation \begin{equation*} \nabla \cdot \left[ \frac{\nabla u}{(1 + |\nabla u|^2)^{1/2}} \right]…
We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
Given a connected compact Riemannian manifold $(M,g)$ without boundary, $\dim M\ge 2$, we consider a space--time fractional diffusion equation with an interior source that is supported on an open subset $V$ of the manifold. The…
The work is devoted to the study of the inverse problem of determining the right-hand side of a nonlinear subdiffusion equation with a Caputo derivative with respect to time. Nonlinearity of the equation means that the right-hand side of…
In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…
Recent results on the maximization of the charged-particle action I in a globally hyperbolic spacetime are discussed and generalized. We focus on the maximization of I over a given causal homotopy class C of curves connecting two causally…
We consider a smooth Riemannian metric tensor $g$ on $\R^n$ and study the stochastic wave equation for the Laplace-Beltrami operator $\p_t^2 u - \Delta_g u = F$. Here, $F=F(t,x,\omega)$ is a random source that has white noise distribution…
We address the inverse Frobenius--Perron problem: given a prescribed target distribution $\rho$, find a deterministic map $M$ such that iterations of $M$ tend to $\rho$ in distribution. We show that all solutions may be written in terms of…
We are concerned with increasing stability in the inverse source problems for the time-dependent Maxwell equations in R^3 , where the source term is compactly supported in both time and spatial variables. By using the Fourier transform,…
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
This paper investigates an inverse random source problem for the stochastic fractional Helmholtz equation. The source is modeled as a centered, complex-valued, microlocally isotropic generalized Gaussian random field whose covariance and…
This paper is concerned with the uniqueness on two inverse moving source problems in electrodynamics with partial boundary data. We show that (1) if the temporal source function is compactly supported, then the spatial source profile…
Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…
We study inverse problems for the nonlinear wave equation $\square_g u + w(x,u, \nabla_g u) = 0$ in a Lorentzian manifold $(M,g)$ with boundary, where $\nabla_g u$ denotes the gradient and $w(x,u, \xi)$ is smooth and quadratic in $\xi$.…
We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…
In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…