Energy Estimates for a Class of High-Order Hyperbolic Equations.

Abstract: The present paper is the first part of an investigation of some problems related to the solvability of high-order hyperbolic equations in spaces of functions bounded or almost-periodic with respect to time variable t. High-order operators are treated under the additional condition on lower terms: the full symbol of the operator has no zeros in a strip δ-< lmτ <δ+, where τ and t are dual variables, and δ±can assign the value ±∞. In this context Leray's separating operator method is developed and two-sided energy estimates in the case of constant coefficients are obtained. These estimates are extended to the operators with variable coefficients if the derivatives of the coefficients are sufficiently 'small''.Note: Research direction:Mathematical problems and theory of numerical method

A numerical method of conformal map of a circular annulus onto the double-connected domain

Abstract: The paper is a continuation of [1] and is devoted to the development of an efficient numerical algorithm for computation of the conformal map of a circular annulus onto the given double- connected domain with the smooth boundary. The quotient of the radii of the annulus (the so-called the conformal radius) is not known in advance and can be calculated by means of numerical analysis of the conformal map of our domain onto a circular annulus [1]. The method of the paper is a generalization of K.I. Babenko’s approach to the numerical conformal map of a circle onto a given simply-connected domain.Note: Research direction:Mathematical problems and theory of numerical method