Ivasyuk H. P.
Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 650-671
We consider initial-value problems for a new class of systems of equations that combine the structures of Solonnikov parabolic systems and Eidel’man parabolic systems. We prove a theorem on the correct solvability of these problems in Hölder spaces of rapidly increasing functions and obtain an estimate for the norms of solutions via the corresponding norms of the right-hand sides of the problem. For the correctness of this estimate, the condition of the parabolicity of the system is not only sufficient but also necessary.
Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1501–1510
We consider a new class of systems of equations that combine the structures of Solonnikov and Éidel’man parabolic systems. We prove a theorem on the reduction of a general initial-value problem to a problem with zero initial data and a theorem on the correct solvability of an initial-value problem in a model case.