Related papers: Inverse Scattering and Stability Estimates for The…
In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…
We study an inverse boundary value problem for a polyharmonic operator in two dimensions. We show that the Cauchy data uniquely determine all the anisotropic perturbations of orders at most $m-1$ and several perturbations of orders $m$ to…
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…
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…
We show that a steady-state solution ${\bf U}$ to the system of equations of a Navier-Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator $\cal L$ has a part of the spectrum in the half-plane…
The inverse problem for the differential operator pencil with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…
We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…
This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that…
In this paper, a diffusion operator including conformable fractional derivatives of order {\alpha} ({\alpha} in (0,1)) is considered. The asymptotics of the eigenvalues, eigenfunctions and nodal points of the operator are obtained.…
We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
In this paper, the Sturm-Liouville operators on a graph with a cycle are considered. We study the inverse spectral problem, which consists in the recovery of the potentials from several spectra and a sequence of signs related to the…
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…
We consider the operator $H:= i \partial_t + \nabla \cdot (c \nabla)$ in an unbounded strip $\Omega$ in $\mathbb{R}^2$, where $c(x,y) \in \mathcal{C}^3(\bar{\Omega})$. We prove adapted a global Carleman estimate and an energy estimate for…
The inverse scattering problem for the two-dimensional nonlinear Klein-Gordon equation $u_{tt}-\Delta u + u = \mathcal{N}(u)$ is studied. We assume that the unknown nonlinearity $\mathcal{N}$ of the equation satisfies $\mathcal{N}\in…
The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…
In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…