Related papers: Unique determination of the damping coefficient in…
We use Coronal Multi-channel Polarimeter (CoMP) observations of propagating waves in the solar corona and Bayesian analysis to assess the evidence of models with resonant damping and foot-point wave power asymmetries. Two nested models are…
This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If…
In this paper, we study the stability in the inverse problem of determining the time dependent absorption coefficient appearing in the linear Boltzmann equation, from boundary observations. We prove in dimension $n\geq 2$, that the…
In this paper, a class of variable-coefficient wave equations equipped with time-dependent damping and the nonlinear source is considered. We show that the total energy of the system decays to zero with an explicit and precise decay rate…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
This paper is concerned with the uniqueness in inverse acoustic scattering problems with the modulus of the far-field patterns co-produced by the obstacle (resp. medium) and the point sources. Based on the superposition of point sources as…
We consider a second-order hyperbolic equation on an open bounded domain $\Omega$ in $\mathbb{R}^n$ for $n\geq2$, with $C^2$-boundary $\Gamma=\pa\Omega=\bar{\Gamma_0\cup\Gamma_1}$, $\Gamma_0\cap\Gamma_1=\emptyset$, subject to…
Decay rates for the energy of solutions of the damped wave equation on the torus are studied. In particular, damping invariant in one direction and equal to a sum of squares of nonnegative functions with a particular number of derivatives…
Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has…
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.
In this paper we study the stability of two different problems. The first one is a one-dimensional degenerate wave equation with degenerate damping, incorporating a drift term and a leading operator in non-divergence form. In the second…
We consider an inverse problem of determining a coefficient $p(x)$ of an evolution equation $\sigma\ppp_tu = a(x)\ppp_x^2u - p(x)u$ for $0<x<\ell$ and $0<t<T$, where $\sigma \in \C \setminus \{0\}$, $\ell>0$ and $T>0$ are arbitrarily given.…
We give a way to recover time-dependent singular coefficients of the wave-equation in the one-dimensional case.
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…
We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…
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…
We are concerned with the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. We establish stability estimates of logarithmic type when the measurements…
This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the…