Related papers: On the determination of the boundary impedance fro…
We introduced in [arXiv:1106.3204] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic Neumann-to-Dirichlet operator. Here we extend the method for sound hard…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
The problem of finding boundary conditions for fastening of a ring membrane, which are inaccessible for direct observation from the natural frequencies of its flexural oscillations, is considered. Two theorems on the uniqueness of this…
We give an iterative method to estimate the disturbance of semi-wavefronts of the equation: $\dot{u}(t,x) = u''(t,x) +u(t,x)(1-u(t-h,x)),$ $x \in \mathbb{R},\ t >0;$ where $h>0.$ As a consequence, we show the exponential stability, with an…
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of…
We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…
We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all…
In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
An inverse obstacle problem for the wave equation in a two layered medium is considered. It is assumed that the unknown obstacle is penetrable and embedded in the lower half-space. The wave as a solution of the wave equation is generated by…
In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…
We investigate the theoretical impedance equations for several near-field antenna positions. In the standard model one computes the currents at the antennas for given voltages using the impedance matrix of the antennas, which is only…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…
We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…