Kovarz I. The mathematical models investigation of space-time systems with delay.

The Thesis is dedicated to obtaining solutions and investigation stability of equation, which describe space-time systems with delay. These models describe adequately the dynamics of complex real processes, if a space multiplier and time delay are taken into account. The boundary problems for parabolic and hyperbolic equations with retarded argument are considered. The special functions such as "delayed exponent", "delayed sine" and "delayed cosine" are introduced to obtain analytical solutions. The theorems on existence and uniqueness of solutions are proved for considered examples. The investigation method of solution stability of differential equation with distributed constants has been developed. The constructive conditions of solution stability have been defined for some classes of space-time systems with delay. Algorithms of control construction for some classes of examined problems have been proposed too. The results, obtained during numerical experiments on nuclear reactor models, which describe neutron diffusion, confirm the theoretical study of delay effect on sustainability process. Key words: boundary problem, hyperbolic partial differential equation, parabolic partial differential equation, delay, convergent series, quasi polynomial, asymptotic stability, measure, model.