arXiv subjects

Aleksandr Murach

Publications and source records attributed to Aleksandr Murach.

20 records · Page 2Linked to original sources

arXiv2017

Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces

In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the operators corresponding to these problems are isomorphisms between appropriate Hörmander spaces. The regularity of the functions which form these spaces is characterized by a pair of number parameters and a function parameter varying regularly at infinity in the sense of Karamata. Owing to this function parameter, the Hörmander spaces describe the regularity of functions more finely than the anisotropic Sobolev spaces.

math.AP↗

arXiv2017

A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems

We consider the most general class of linear boundary-value problems for ordinary differential systems, of order $r\geq1$, whose solutions belong to the complex space $C^{(n+r)}$, with $0\leq n\in\mathbb{Z}$. The boundary conditions can contain derivatives of order $l$, with $r\leq l\leq n+r$, of the solutions. We obtain a constructive criterion under which the solutions to these problems are continuous with respect to the parameter in the normed space $C^{(n+r)}$. We also obtain a two-sided estimate for the degree of convergence of these solutions.

math.CA↗