相关论文: Schiffer's Conjecture, Interior Transmission Eigen…

We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…

In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which…

The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…

This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data…

This article studies an inverse problem for a transmission wave equation, a system where the main coefficient has a variable jump across an internal interface given by the boundary between two subdomains. The main result obtains Lipschitz…

This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…

We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the…

The two-dimensional sloshing problem is considered; it describes the transversal free oscillations of water in an open, infinitely long canal of uniform cross-section. It is proved that the fundamental eigenfrequency is simple, whereas the…

The inverse problem of finding the refraction coefficient of a shallow ocean from the observation of the extra Cauchy data for the acoustic field at the surface of the ocean is studied. Uniqueness theorem is proved and a reconstruction…

This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant…

The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…

In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete, if the electromagnetic parameters $\eps, \, \mu,…

In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff--Love infinite plate problem.…

Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The…

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Hele-Shaw problems are prototypes to study the interface dynamics. Linear theory suggests the existence of self-similar patterns in a Hele-Shaw flow. That is, with a specific injection flux the interface shape remains unchanged while its…

We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order term. The medium is characterized by a spatially varying…

This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…