On spectral properties of the Laplace operator via boundary perturbation.
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On the acoustic impedence condition for ondulated boundary
On the Relative Completeness of the Generalized Eigenvectors of Elliptic Eigenvalue Problems with Indefinite Weight Functions.
Optimal energy decay rate of coupled wave equations.
Periodic Solutions of a Nonlinear Wave Equation Without Assumption of Monotonicity.
Perturbatively unstable eigenvalues of a periodic Schrödinger operator.
Pointwise Fourier Inversion on Tori and Other Compact Manifolds.
Polynomial boundedness of eigensolutions and the spectrum of Schrödinger operators.
Regular eigenvalue problem with eigenparameter contained in the equation and the boundary conditions.
Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators
We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in norm, at Lebesgue points and almost everywhere. We also prove localization results.
Scattering for a dispersive charge transfer model
Semiclassical eigenstates in a multidimensional well
Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains
Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order
We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].
Spectral analysis of non-self-adjoint elliptic operators
Spectral Analysis of the Laplacian in Distorted Periodic Waveguides.
Spectral Analysis of the Laplacian in Domains with Cylinders.
Spectral properties of a solution to the Gellerstedt problem for mixed-type equations and their applications.