Volume 48, № 2, 1996
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 147-160
We construct uniform asymptotics for a solution of a system of singularly perturbed differential equations with turning point. We consider the case where the boundary operator analytically depends on a small parameter.
Global solutions of a two-dimensional initial boundary-value problem for a system of semilinear magnetoelasticity equations
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 161-167
We prove the theorem on the existence and uniqueness of global solutions of a system of semilinear magnetoelasticity equations in a two-dimensional space.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 168-183
We obtain a criterion of completeness of a system of exponentials in the Hardy-Smirnov spaces in unbounded convex polygons and study the properties of incomplete systems of exponentials.
Representation and investigation of solutions of a nonlocal boundary-value problem for a system of partial differential equations
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 184-194
We study the boundary-value problem for a system of partial differential equations with constant coefficients with conditions nonlocal in time. By using a metric approach, we prove the well-posedness of the problem in the scale of Sobolev spaces of functions periodic in space variables. By using matrix calculus, we construct an explicit representation of a solution.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 195-201
We prove the maximum principle and various modifications of it for one class of degeneration of parabolic equations.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 202-211
For thermal and diffusion processes in active media described by nonlinear evolution equations, we study the phenomena of space localization and stabilization for finite time.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 212-219
We propose a new scheme of discretization of the Lavrent’ev method for operator equations of the first kind with self-adjoint nonnegative operators of certain “smoothness.” This scheme is more economical in the sense of the amount of used discrete information as compared with traditional approaches.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 220-235
We construct a hierarchy of Poisson Hamiltonian structures related to an “elliptic” spectral problem and determine the generating operators for the equation of asymmetric chiral 0 (3) — field.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 236-250
We obtain estimates of the best polynomial approximations, uniform in the closure $B$ of Faber domains of the complex plane $ℂ$, for functions continuous in $B$ and defined by Cauchy-type integrals with densities possessing certain generalized differential properties. We establish estimates exact in order for the Kolmogorov widths of classes of such functions in relevant functional spaces.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 251-259
We describe normal congruences of group isotopes, establish criteria of homomorphism and isomorphism, and select the methods for description of isotopes up to isomorphism. In addition, we establish a criterion for a subset to be a subquasigroup of a group isotope and describe subquasigroups of certain classes of group isotopes. The obtained results are applied to the investigation of left distributive quasi-groups.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 260-277
We study the problem of strong summability of Fourier series in orthonormal systems of polynomial-type functions and establish local characteristics of the points of strong summability of series of this sort for summable functions. It is shown that the set of these points is a set of full measure in the region of uniform boundedness of systems under consideration.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 278-284
For linear difference equations in the space of bounded number sequences, we prove an analog of the Erugin theorem on reducibility and present sufficient conditions for the reducibility of countable linear systems of difference equations with periodic coefficients.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 285-286
Application of ateb-functions to the construction of solutions of some nonlinear partial differential equations
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 287-288
We construct asymptotic approximations of one-frequency solutions of some nonlinear partial differential equations by using periodic Ateb-functions.