Ivasyuk G. Initial problems for Solonnikov-Eidelman's parabolic systems

A class of Solonnikov-Eidelman's parabolic systems. For this class of systems it is described a statement of Solonnikov-Eidelman's parabolic initial problems (SEPIP). For model SEPIP a structure of fundamental matrix of solutions is defined, its estimates are obtained and the theorem on correct resolvability in Holder spaces of increasing functions, is proved. For common SEPIP a theorem on correct resolvability in Holder spaces of increasing functions, similar to the corresponding theorem for model case, is proved. It is proved, that the parabolic condition for systems is necessary condition for correctness of a priori estimates in Holder spaces of solutions common SEPIP.