Початковi задачi для параболiчних систем Солонникова–Ейдельмана

Abstract

Initial problems for a new class of systems, which unite the structures of Solonnikov-parabolic and Eidelman-parabolic systems, are considered. The theorem on a correct solvability of these problems in Holder spaces of rapidly growing functions is proved, and an estimate of the norms of solutions through the corresponding norms of right-hand members of a problem is obtained. For a correctness of such an estimate, the requirement of parabolicity of a system is not only sufficient, but also necessary.