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A series of the work «Modeling of thermal and wave processes on the basis of boundary and non-local problems»

Work number - M 72 FILED

Authors: ChernenkoVarvaraPetrоvna, KobilskayaЕlenaBorisovna

Submittedby KremenchukNational University named MykhailoOstrohradskyi

Series of scientific works consists of four monographs and 26 scientific papers published during 2005–2013 years.

Newclassesofmathematicalmodelsofthermalandwaveprocessesinthemoving andstationarymediumsintheformofboundaryandnonlocalproblemsforequationsofparabolicandhyperbolictypearebuilt.The solutions ofthese problems in the design of equipment and electroplastic and electroimpulse materials processing are used.

Several fundamental results in the field of mathematical modeling of wave and thermal processes areobtained.Namely, the most complete mathematical models of thermal processes that occur in the moving and the stationary mediums; the wave processes in the thin rods and shells are developed; the methodsand researches of the problems that describe the proposed models are improved.

The constructed mathematical models take into account the features of functions of heat source in the nonlocal and non-linear boundary problems for the wave equation and the heat equation. It is possible to find the parameters control of temperature fields during the process of electroplastic and electroimpulse processing of metals that belong to a class of energy-saving. The asymptotic methods of the non-stationary problems for the hereditary elastic rods and cylindrical shells with increasing time are developed. It allows to predict the mechanical behavior of the new materials and it allows to describe  the reaction of the material or constructionon a wide range of external influences.

The unique existence theorem of solutionof the nonlocal and boundary  problems for the heat equation are formulated and proved.

Cycle results are significant contribution to the development of the theory of mathematical modeling, the theoryand research methods for solving the boundary and nonlocal problems of the equations of mathematical physics. The results, which obtained in the work, can be used for further development of the general theory of mathematical modeling with the use of nonlocal and boundary problems.

The research results of topic work set out in the 4 monographs,26 articles(including three foreign editions, 1 contained in the SCOPUS database), 35 abstracts.

The total number of publications of authors is 65 works.