Kukharenko O. Modeling of linear-distributed systems with an aftereffect

The aim of the thesis is devoted to studying of mathematical models described by systems of delay partial differential equations. The special functions, called the delay exponential function, delay cosine and delay sine were used for solving the Cauchy problem for linear stationary delay equations of the first and second order. Using an iteration process two linear-independent solutions were obtained for the linear stationary delay equation of the second order with phase coordinate without and with delay . Using results obtained for ordinary equations, systems of partial differential equations of the first order were considered. The Cauchy problem was solved for the systems of equations with one constant delay. The cases of systems of equations with delay in phase coordinates, in the derivatives of the phase coordinates, and with pure delay are considered. Then the first boundary value problem was solved for the system of the delay parabolic equations for the different cases of delays. Theorems of converges of the obtained solutions are proofed. The finite control problems were solved for the systems of parabolic delay equations. Also the systems of the hyperbolic equations were studied and the control problems for such systems were solved.