Related papers: Variations of thin piezoelectric shallow shells: T…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of…
A method based on the envelope theory is presented to compute approximate solutions for $N$-body Hamiltonians with identical particles in $D$ dimensions ($D\ge 2$). In some favorable cases, the approximate eigenvalues can be analytically…
In this paper we prove that the smallest eigenvalue $\lambda_1$ of the eigenvalue problem for a quasilinear elliptic systems introduced by de Th\'elin in \cite{DT}, is not only simple (in a suitable sense), but also isolated. Moreover, we…
We study small, PT-symmetric perturbations of self-adjoint double-well Schr\"odinger operators in dimension $n\geq 1$. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the…
The quantum eigenvalue problem arises in the study of the geometric measure of the quantum entanglement. In this paper, we convert the quantum eigenvalue problem to the Z-eigenvalue problem of a real symmetric tensor. In this way, the…
A Hamiltonian treatment of the gravitational collapse of thin shells is presented. The direct integration of the canonical constraints reproduces the standard shell dynamics for a number of known cases. The formalism is applied in detail to…
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…
The behaviour of sloshing eigenvalues and eigenfunctions is studied for vertical cylindrical containers that have circular walls and constant (possibly infinite) depth. The effect of breaking the axial symmetry due to the presence of radial…
We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of…
Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the solution of three transcendential equations for three unknown numbers, moduli of pants. The complete list of antisymmetric eigenfunctions of integral equation in…
A two dimensional eigenvalue problem (2DEVP) of a Hermitian matrix pair $(A, C)$ is introduced in this paper. The 2DEVP can be viewed as a linear algebraic formulation of the well-known eigenvalue optimization problem of the parameter…
This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates. Viewing this problem as a quasilinear dispersive…
We consider a family of linear viscoelastic shells with thickness $2\varepsilon$ ( $\varepsilon$ , small parameter), clamped along a portion of their lateral face, all having the same middle surface $S$. We formulate the three-dimensional…
We study the eigenvalue problem $-u"+V(z)u=\lambda u$ in the complex plane with the boundary condition that $u(z)$ decays to zero as $z$ tends to infinity along the two rays $\arg z=-\frac{\pi}{2} \pm \frac{2\pi}{m+2}$, where…
Analytic solutions for the energy eigenvalues are obtained from a confined potentials of the form $br$ in 3 dimensions. The confinement is effected by linear term which is a very important part in Cornell potential. The analytic eigenvalues…
It is known that every positive solution of a one-dimensional Gel'fand problem can be written explicitly. In this paper we obtain exact expressions of all the eigenvalues and eigenfunctions of the linearized eigenvalue problem at each…
We consider a spectral problem associated with steady water waves of extreme form on the free surface of a rotational flow. It is proved that the spectrum of this problem contains arbitrary large negative eigenvalues and they are simple.…
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…