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Qualitative analysis and numerical methods for hereditary systems



A.V. Anikushyn, A.L. Hulianytskyi.


Submitted by the Faculty of Cybernetics of Taras Shevchankon National University of Kyiv


The series of scientific works consists of 1 work-book, 1 monograph, 16 scientific papers and 22 conference talks.

For a number of classes of hereditary distributed parameter systems, we prove a set of theoretical results concerning generalized solvability and convergence of Galerkin’s approximations.

We study elliptic, parabolic, and hyperbolic integro-differential equations, as well as equations with nonnegative-definite integral operators, including those of high order. We establish the existence and uniqueness of generalized solutions for initial-boundary value problems for those types of equations. The solvability theorems are proven by employing the a priori estimate method, which is modified according to the specific prorerties of integro-differential equations. The theorems that guarantee the existence of an optimal control (impulse, point, impulse-point etc) are derived directly from the corresponding solvability theorems. For the mentioned intergo-differential equations, as well as for the time-fractional diffusion equation, we obtain the theorems of convergence of the Galerkin approximations. The results obtained in the series of works can be used as theoretical foundations for investigation a broad class of physical, biological and other systems with memory, and also for the optimal control of such systems

The results of research are published in 1 tutorial, 1 monograph, 16 articles (including 2 in foreign journals), and 22 congerence talks.

Total number of the authors’ publications: 1 monograph, 20 articles (including 2 in foreign journals), 1 work-book, 16 training tools, and 26 conference talks.