Dovzhytska I. Cauchy problem for parabolic systems of Shilov type with variable coefficients and nonnegative genus

The thesis is devoted to investigation of Cauchy problem for parabolic systems of Shilov type with variable coefficients and nonnegative genus. We defined a new class of parabolic systems of equations with partial derivatives with bounded smooth variable coefficients. We constructed the fundamental matrix of solutions to the Cauchy problem and investigated its basic properties. In the case of initial data being distributions of Gelfand-Shilov type we established the correct solvability of the Cauchy problem. We investigated the localization and stabilization properties of solutions to the Cauchy problem and proved the theorem of Liouville type.