The total boundary value problems for hiperbolic equation with piecewise continuous coefficients and right parts
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 2
Abstract
In this paper, the general boundary value problems for hyperbolic equation with piecewise continuous on spatial variable coefficients and right parts was considered. The solutions such problems were found by using a concept of quasi-derivatives, a modern theory of systems of linear differential equations, the classical Fourier method and a reduction method.
Authors and Affiliations
R. M. Tatsij, O. Yu. Chmyr, O. O. Karabyn
Asymptotic representations of the solutions with slowly varying derivatives of second order essential nonlinear differential equations
The asymptotic representations, necessary and sufficient conditions of the existence of the solutions with slowly varying derivatives are found for differential equations of the second order that are in some sense simila...
DIVISORS OF THE GAUSSIAN INTEGERS IN NORM GROUP E+ 𝑁
The divisor function in norm group E+ 𝑛 is investigated, where the set E+ 𝑛 is a multiplicative subgroup in the multiplicative group of classes of residues modulo 𝑝𝑛 over Z[𝑖]. The asymptotic formula is obtained. MSC: 11...
THE ANALOGUE OF THE FLOQUET-LYAPUNOV THEOREM FOR THE LINEAR DIFFERENTIAL SYSTEMS OF THE SPECIAL KIND
The analogue of the well known in the theory of the linear differential systems Floquet's--Lyapunov's theorem are constructed by the certain condidtions for the linear differential system, whose coefficients are represen...
ON THE STRUCTURE OF THE FUNDAMENTAL MATRIX OF THE LINEAR HOMOGENEOUS DIFFERENRIAL SYSTEM OF THE SPECIAL KIND
For the linear homogeneous differenrial system, whose coefficients are represented as an absolutely and uniformly convergent Fourier-series with slowly varying coefficients and frequency, the kind of the fundamental matr...
SYSTEMS OF LINEAR CONTROLLED DIFFERENTIAL EQUATIONS WITH VARIABLE DIMENSION
The article investigates the linear control system of variable dimension. The optimal control problem for several objects with a consistent in time mode of their operation is considered. The initial state of each object...