Related papers: Inverse problems for semilinear wave equations on …
We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…
In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
In the Hilbert space $H$, the inverse problem of determining the right-hand side of the abstract subdiffusion equation with the fractional Caputo derivative is considered. For the forward problem, a non-local in time condition $u(0)=u(T)$…
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…
The existence of co-rotational finite time blow up solutions to the wave map problem from R^{2+1} into N, where N is a surface of revolution with metric d\rho^2+g(\rho)^2 d\theta^2, g an entire function, is proven. These are of the form…
We study inverse scattering for $\Delta_g+V$ on $(X,g)$ a conformally compact manifold with metric $g,$ with variable sectional curvature $-\alf^2(y)$ at the boundary and $V\in C^\infty(X)$ not vanishing at the boundary. We prove that the…
For a given smooth compact manifold $M$, we introduce an open class $\mathcal G(M)$ of Riemannian metrics, which we call \emph{metrics of the gradient type}. For such metrics $g$, the geodesic flow $v^g$ on the spherical tangent bundle $SM…
As a prototype of an evolution equation we consider the Schr\"odinger equation i (d/dt) \Psi(t) = H \Psi(t), H = H_0 + V(x) for the Hilbert space valued function \Psi(.) which describes the state of the system at time t in space dimension…
Wind speed measurements using heterodyne lidars are limited in spatial resolution because of the current signal processing methods. This limit is equal to c $\tau$ ( c is the speed of light and $\tau$ is the laser pulse duration)…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…
We are concerned with the well-posedness of an inverse problem for determining the wedge boundary and associated two-dimensional steady supersonic Euler flow past the wedge, provided that the pressure distribution on the boundary surface of…
Consider two inverse problems for Sturm-Liouville problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq 2$, with boundary $\partial M$, we consider an initial boundary value problem for a fractional diffusion equation on $(0,T) \times M$, $T>0$, with time-fractional…