Mathematics

2005, No. 3

O.V. Bespolitov

DISCRETE ORTHOGONAL TRANSFORMATIONS WITH "NOISE-LIKE" BASIS FUNCTIONS

The paper is devoted to discrete orthogonal transformations with noise-like basis functions. During information transfer energetically important components loss is possible. Thus transformations which don’t posses properties of energy concentration in several spectral components are proposed.

L.M. Berkovich, A.N. Lepilov

INVARIANT SOLUTIONS OF THE NONLINEAR HEAT CONDUCTION EQUATION

In the paper self-similar solutions (exact and asymptotic) of the nonlinear heat conduction equation are obtained by using group analysis technique and exact linearization of differential equations. The obtained solutions describe both the processes of blow-up and travelling wave.

A.M. Dzhurayev

INITIAL VALUE PROBLEM FOR A SYSTEM OF TWO SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS WITH A MULTIPLE PURE IMAGINARY SPECTRUM

In the paper a new asymptotic integration method for a system of two singularly perturbed differential equations with multiple pure imaginary spectrum is proposed. The initial value problem under stable spectrum conditions is studied. The solvability theorems are proved and the residual term estimation is given.