相关论文: Nonradiating sources and transmission eigenfunctio…
In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary,…
This paper is concerned with non-radiating elastic sources in inhomogeneous elastic media. We demonstrate that the value of non-radiating elastic sources must vanish at convex corners of their support, provided the sources exhibit H\"older…
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…
The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$, $n=2,3$. Second, we…
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…
This paper offers an extensive exploration of nonradiating sources for the two- and three-dimensional biharmonic wave equations. Various equivalent characterizations are derived to reveal the nature of a nonradiating source. Additionally,…
In this paper, we consider the transmission eigenvalue problem associated with a general conductive transmission condition and study the geometric structures of the transmission eigenfunctions. We prove that under a mild regularity…
Let $\Omega$ be a bounded domain in $\mathbb{R}^n$, $n\geq 2$, and $V\in L^\infty(\Omega)$ be a potential function. Consider the following transmission eigenvalue problem for nontrivial $v, w\in L^2(\Omega)$ and $k\in\mathbb{R}_+$,…
This paper is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in [9]. It is shown in two scenarios that the…
We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves, interior transmission eigenfunctions, and their applications to…
This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects.…
We consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, we show that the singularities which are diffracted by the corners…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
Given near or far field wave measurements generated by some unknown time- and space-dependent acoustic source, we seek to rapidly determine a domain in space-time, as small as possible, that contains the support of a source radiating these…
In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is…
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…
This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact…