Unguryan G. The Cauchy problem for parabolic systems by Shilov with non-negative genus and coefficients of bounded smoothness

The dissertation is devoted to the study of the Cauchy problem for parabolic systems by Shilov with non-negative genus and coefficients of bounded smoothness. A new class of parabolic systems of equations with partial derivatives and coefficients of limited smoothness is indicated. A fundamental matrix of solutions of the Cauchy problem was constructed and there is main properties were investigated. A correct solvability of the Cauchy problem is established in the case when the initial data are generalized functions of the distribution type of Gelfand and Shilov. The principle of localization is established, a comparative analysis results obtained with known results was conducted. The obtained results are demonstrated on the model example.