Litovchenko V. Correct solvability of Cauchy problem for parabolic pseudodifferential systems in the spaces of infinitely derived functions

An object is the Cauchy problem (CP) for the new classes of parabolic of the pseudodifferential systems (PDS); the purpose – extends and generalization of the known classes of the parabolic systems of partial differential equations with quotients by derivatives (SDEPD) and construction of theory of correct solvablity СР; the methods of researches are the developed classic methods theories of spaces basic and generalized functions, and also theories CP for the linear parabolic systems. The new and results is new classes of parabolic PDS equalizations of the first order on t with protuberant to the different degree of smoothness by characters pseudodifferentiations, which have classes of Petrovskogo, Eidelmana, Shilova and Matiychuka SDEPD; theory of correct solvability CP for these classes in spaces infinitely differentiable functions. The field is mathematic and physic.