3 papers
math.AP2024
On the Classicality of Solutions to a Boundary Value Problem for a Second-Order Parabolic System
O. V. Diachenko, V. M. Los
We study a parabolic initial-boundary-value problem for a system of two differential equations with two boundary conditions of different orders, the Dirichlet and Neumann ones. It…
math.AP2022
Regularity conditions for solutions to some parabolic systems
Oleksandr Diachenko, Valerii Los
We investigate global and local regularity of generalized solutions to parabolic initial-boundary value problem for Petrovskii system of second order differential equations. Result…
math.AP2021
Some problems for Petrovskii parabolic systems in generalized Sobolev spaces
Aleksandr Dyachenko, Valerii Los
We consider an inhomogeneous initial-boundary value problem for a Petrovskii parabolic system of second order PDEs. We prove that this problem induces isomorphisms between appropri…