Vlasenko L. Mathematical modeling of systems and processes with using implicit and degenerate evolution equations

The dissertation is devoted to the development of mathematical modeling methods of systems and processes to electrodynamics, radio engineering, thermal physics, liquid filtration and synthesis of corresponding mathematical models, to the development of the theory of different classes of implicit and degenerate evolution equations, which arise under constructing mathematical models, and its application to the development of instruments for analysis of constructed mathematical models and corresponding numerical methods. The theory of different classes of implicit and degenerate evolution equations, in particular, differential operator equations of high order, differential difference and difference equations, functional differential equations, impulsive differential equations, have been developed. Applications of obtained theoretical results to analyzing systems and processes whose mathematical models contain implicit and degenerate equations have been realized.