On the solvability in a weighted space of an initial–boundary value problem for a third-order operator-differential equation with a parabolic principal part
- Authors: Aliev A.R.1,2, Lachinova F.S.3
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Affiliations:
- Baku State University
- Institute of Mathematics and Mechanics
- Azerbaijan State University of Oil and Industry
- Issue: Vol 93, No 1 (2016)
- Pages: 85-88
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223405
- DOI: https://doi.org/10.1134/S1064562416010294
- ID: 223405
Cite item
Abstract
In a Sobolev-type space with an exponential weight, sufficient conditions are obtained for the correct and unique solvability of an initial–boundary value problem for a third-order operator-differential equation with a parabolic principal part having a multiple characteristic. The conditions are expressed in terms of the operator coefficients of the equation. Additionally, the norms of the operators of intermediate derivatives associated with the solvability conditions are estimated. The relation between the weight exponent and the lower boundary of the spectrum of the basic operator involved in the principal part of the equation is established. The results are illustrated as applied to a mixed problem for partial differential equations.
Keywords
About the authors
A. R. Aliev
Baku State University; Institute of Mathematics and Mechanics
Author for correspondence.
Email: alievaraz@yahoo.com
Azerbaijan, ul. Z. Khalilova 23, Baku, AZ1148; ul. B. Vakhabzade 9, Baku, AZ1141
F. S. Lachinova
Azerbaijan State University of Oil and Industry
Email: alievaraz@yahoo.com
Azerbaijan, pr. Azadlig 20, Baku, AZ1010