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We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface…
This review is dedicated to some recent results on Weyl theory, inverse problems, evolution of the Weyl functions and applications to integrable wave equations in a semistrip and quarter-plane. For overdetermined initial-boundary value…
The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly oscillating coefficients and with indefinite (sign-changing) density function is investigated in periodically perforated…
The Steklov problem is an eigenvalue problem with the spectral parameter in the boundary conditions, which has various applications. Its spectrum coincides with that of the Dirichlet-to-Neumann operator. Over the past years, there has been…
We consider the propagation of waves in a waveguide with Neumann boundary conditions. We work at low wavenumber with only one propagating mode in the leads, all the other modes being evanescent. We assume that the waveguide is symmetric…
In this paper, we investigate the sampling analysis associated with discontinuous Sturm-Liouville problem which has transmission conditions at two points of discontinuity also contains an eigenparameter in a boundary condition and two…
Connections between the electron eigenstates and conductivity of one-dimensional disordered electron systems is studied in the framework of the tight-binding model. We show that for weak disorder only part of the states exhibit resonant…
In this paper, we investigate the scattering of surface waves on reactive impedance boundaries when the surface impedance undergoes a sudden change in time. We report three exotic wave phenomena. First, it is shown that by switching the…
Experiments have shown that micron-sized distributed surface roughness can significantly promote transition in a three-dimensional boundary layer dominated by crossflow insta- bility. This sensitive effect has not yet been fully explained…
Given a set of transmission eigenvalues, its density function inversely determines the form of the indicator function. This is one application of the Cartwright's theory in inverse problems. We use the indicator function inversely to…
The distribution of eigenvalues of the wave equation in a bounded domain is known as Weyl's problem. We describe several computational projects related to the cumulative state number, defined as the number of states having wavenumber up to…
For bounded domains, eigenvalues and eigenfunctions of double layer potentials are considered. The aim of this paper is to establish some relationships between eigenvalues, eigenfunctions and the geometry of domain boundaries.
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This…
We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domain-wise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard…
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…
The physical interpretation of the appearance of resonant transmission through single-point barriers is discussed on the basis of a double-layer heterostructure in the squeezing limit as both the thickness of the layers and the distance…
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…
We investigate an inverse scattering problem for a thin inhomogeneous scatterer in R^m, m = 2,3, which we model as a m-1 dimensional open surface. The scatterer is referred to as a screen. The goal is to design target signatures that are…
We study the asymptotic behaviour of eigenvalues and eigenfunctions of a boundary value problem for the Sturm-Liouville operator with general boundary conditions and the weight function perturbed by the so-called $\delta'$-like sequence…
We study concentration operators associated with either the discrete or the continuous Fourier transform, that is, operators that incorporate a spatial cut-off and a subsequent frequency cut-off to the Fourier inversion formula. Their…