On some unilateral boundary value problems for the von Kármán equations. Part I: The coercive case
On some variational inequalities for nonclassical type operators
The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.
On some weighted inequalities of the qualitative theory of elliptic equations.
On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes
This article is devoted to the discretization of source terms and boundary conditions using discontinuous Galerkin schemes with an arbitrary high order of accuracy in space and time for the solution of hyperbolic conservation laws on unstructured triangular meshes. The building block of the method is a particular numerical flux function at the element interfaces based on the solution of Generalized Riemann Problems (GRPs) with piecewise polynomial initial data. The solution of the generalized Riemann...
On spaces and
On Space-Time Means and Strong Global Solutions of Nonlinear Hyperbolic Equations.
On Space-Time Means Everywhere Defined Scattering Operators for Nonlinear Klein-Gordon Equations.
On spatial decay estimates for derivatives of vorticities of the two dimensional Navier-Stokes flow
On spectral approximation. Part 1. The problem of convergence
On spectral approximation. Part 2. Error estimates for the Galerkin method
On spectral projections of elliptic operators
On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials
On spectral properties of the Laplace operator via boundary perturbation.
On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆
We study the spectral stability of solitary wave solutions to the nonlinear Dirac equation in one dimension. We focus on the Dirac equation with cubic nonlinearity, known as the Soler model in (1+1) dimensions and also as the massive Gross-Neveu model. Presented numerical computations of the spectrum of linearization at a solitary wave show that the solitary waves are spectrally stable. We corroborate our results by finding explicit expressions for...
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 splitting up singularities of fundamental solutions to elliptic equations in ℂ2
It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.
On Squeezing and Flow of Energy for Nonlinear Wave Equations.
On stability and growth of solutions for classes of initial and boundary value problems
On stability of axially symmetric solutions to Navier-Stokes equations in a cylindrical domain and with boundary slip conditions
The existence of global regular axially symmetric solutions to Navier-Stokes equations in a bounded cylinder and for boundary slip conditions is proved. Next, stability of these solutions is shown.