The article presents three scenarios of the evolution of spatial-temporal chaos and specifies the corresponding types of chaotic solutions to a certain nonlinear boundary-value problem for PDE. Analytic assertions are ...

A complete asymptotical solution is constructed and justified for optimal singular parabolic problems with constraint control and complete degeneration of the differential part of the operator.

For a sequence of stochastic equations of diffusion type, the conditions, which arc close to necessary and sufficient ones, are found for the weak convergence of measures μ(ξ(n),w),n=1,..., which correspond to solutions, ...

The conditions are investigated for localization of the Bokhner - Riesz averages in the Nikol'skii classes uαp for p∈[1,2].

Розширено класи кривих та заданих функцій в теорії повного сингулярного інтегрального рівняння з ядром Коші та доведено узагальнення класичних теорем Нетера. Як наслідок цих теорем доведено нетеровість асоційованих з ...

Functions are investigated whose integrals over a given collection of sets are zero. Pompeiu sets are described in terms of the approximation of their indicators by linear combinations of the indicators of balls with special ...

Conditions under which there exists a change of variables that decomposes a countable system of differential equations are established for the entire real axis and a semiaxis. Similar problems are investigated for a countable ...

The conditions are established, under which periodic solutions of pulse evolutionary systems with unbounded (inx) operators on the right-hand sides exist and are stable.