Qualitative analysis and numerical methods for hereditary systems

Work number - M 57 ALLOWED TO PARTICIPATE

Authors:

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.

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