Some problems for Petrovskii parabolic systems in generalized Sobolev spaces
Analysis of PDEs
2021-03-31 v1
Abstract
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 appropriate anisotropic generalized Sobolev spaces. The regularity of these spaces are given by a pair of real numbers and by a function parameter. The latter allows us to characterize the regularity of solutions to the problem more finely as compared with anisotropic Sobolev spaces.
Keywords
Cite
@article{arxiv.2103.16474,
title = {Some problems for Petrovskii parabolic systems in generalized Sobolev spaces},
author = {Aleksandr Dyachenko and Valerii Los},
journal= {arXiv preprint arXiv:2103.16474},
year = {2021}
}
Comments
13 pages. arXiv admin note: substantial text overlap with arXiv:1907.04283, arXiv:2006.00553