Weighted Energy Decay for 3D Klein-Gordon Equation

We obtain a dispersive long-time decay in weighted energy norms for solutions of the 3D Klein-Gordon equation with generic potential. The decay extends the results obtained by Jensen and Kato for the 3D Schredinger equation. For the proof we modify the spectral approach of Jensen and Kato to make it applicable to relativistic equations

Competences of a bachelor’s degree in restoration in the context of requirements presented by the society, government and employers to a specialist in this area of activity

The article touches upon the topic of training students at a University of a restoration profile and modern employer’s requirements towards the graduates of such educational institutions. It describes the idea of a occupational competence of a bachelor of restoration and identifies the priorities of socially important professional qualities of a restoration specialistЗатрагивается тема подготовки студентов вуза реставрационного профиля и рассматриваются требования современного работодателя к выпускнику учебного заведения. Дано понятие профессиональной компетенции бакалавра реставрации. Выделены социально значимые профессиональные качества личности реставратор

On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing

Consider the Klein-Gordon equation (KGE) in $\R^n$, $n\ge 2$, with constant or variable coefficients. We study the distribution $\mu_t$ of the random solution at time $t\in\R$. We assume that the initial probability measure $\mu_0$ has zero mean, a translation-invariant covariance, and a finite mean energy density. We also asume that $\mu_0$ satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The main result is the convergence of $\mu_t$ to a Gaussian probability measure as $t\to\infty$ which gives a Central Limit Theorem for the KGE. The proof for the case of constant coefficients is based on an analysis of long time asymptotics of the solution in the Fourier representation and Bernstein's `room-corridor' argument. The case of variable coefficients is treated by using an `averaged' version of the scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay.Comment: 30 page