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In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

One important innovation here is that for the Sturm-Liouville considered equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at one interior point. We develop Green's function…

Classical Analysis and ODEs · Mathematics 2013-03-29 K. Aydemir , O. Sh. Mukhtarov

The paper contains lower bounds on the counting function of the positive eigenvalues of the interior transmission problem when the latter is elliptic. In particular, these bounds justify the existence of an infinite set of interior…

Mathematical Physics · Physics 2015-06-05 Evgeny Lakshtanov , Boris Vainberg

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…

Numerical Analysis · Mathematics 2016-08-24 Fang Zeng , Jiguang Sun , Liwei Xu

In this paper, we study the Helmholtz transmission eigenvalue problem for inhomogeneous anisotropic media with the index of refraction $n(x)\equiv 1$ in two and three dimension. Starting with a nonlinear fourth order formulation established…

Numerical Analysis · Mathematics 2023-04-26 Qing Liu , Tiexiang Li , Shuo Zhang

We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…

Analysis of PDEs · Mathematics 2015-06-11 Mourad Bellassoued , Michel Cristofol , Eric Soccorsi

We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue…

Mathematical Physics · Physics 2012-09-25 Yury Smirnov , Yury Shestopalov

We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material…

Optics · Physics 2017-01-09 R. J. Churchill , T. G. Philbin

In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems…

Classical Analysis and ODEs · Mathematics 2013-04-23 Erdoğan Şen , Oktay Mukhtarov

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Two theorems on strong solvability and the…

Analysis of PDEs · Mathematics 2021-03-12 Abdumauvlen S. Berdyshev

This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission…

Spectral Theory · Mathematics 2015-06-16 Evgeny Lakshtanov , Boris Vainberg

A waveguide coincides with a three-dimensional domain G having finitely many cylindrical outlets to infinity; the boundary of G is smooth. In G, we consider the stationary Maxwell system with real spectral parameter k and identity matrices…

Mathematical Physics · Physics 2012-06-04 B. A. Plamenevskii , A. S. Poretckii

We consider Maxwell's equations in a 3-dimensional material, in which both, the electric permittivity, as well as the magnetic permeability, fluctuate in space. Differently from all previous treatments of the disordered electromagnetic…

In this paper, we consider an interior transmission eigenvalue problem on two compact Riemannian manifolds with common smooth boundary. We suppose that a couple of these manifolds is equipped with locally anisotropic type Riemannian metric…

Spectral Theory · Mathematics 2017-03-14 Naotaka Shoji

In [Camano, Lackner, Monk, SIAM J. Math. Anal., Vol. 49, No. 6, pp. 4376-4401 (2017)] it was suggested to use Stekloff eigenvalues for Maxwell equations as target signature for nondestructive testing via inverse scattering. The authors…

Spectral Theory · Mathematics 2019-09-06 Martin Halla

In this study by applying an own technique we investigate some asymptotic approximation properties of new type discontinuous boundary-value problems, which consists of a Sturm-Liouville equation together with eigenparameter-dependent…

Classical Analysis and ODEs · Mathematics 2013-03-29 O. Sh. Mukhtarov , K. Aydemir

This paper presents a new approach to the two-interval Sturm-Liouville eigenfunction expansions, based essentially on the method of integral equations. We consider the Sturm-Liouville problem together with two supplementary transmission…

Classical Analysis and ODEs · Mathematics 2013-12-12 K. Aydemir , O. Sh. Mukhtarov

In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…

Analysis of PDEs · Mathematics 2018-05-30 Martin Spitz

The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the…

Mathematical Physics · Physics 2010-01-20 Yu. F. Alabina , A. V. Latyshev , A. A. Yushkanov

Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…

Analysis of PDEs · Mathematics 2012-04-26 Lung-Hui Chen