Abstract:
At the end of the nineteenth century A. Poincare began to study equations which were unsolved
with respect to high derivative equations. The systematical study of such equations began in
S. L. Sobolev's works in the second part of the last century. Therefore, such equations are called Sobolev
type equations. The increased interest to Sobolev type equations led to the necessity to consider them in
quasi-Banach spaces.
This article presents the results of the existence of exponential dichotomies of solutions of dynamical Sobolev type equations studied in quasi-Banach spaces.
The relatively spectral theorem and the problem of the existence of invariant solution spaces were
considered. The interest to such solution is explained by the fact that it is the most popular and reflects
experimental data while solving practical tasks.
Besides the introduction and the references the article contains two parts. The first part provides
necessary notions and a relatively spectral theorem in quasi-Banach spaces. The second one represents
the existence of invariant spaces and exponential dichotomies of solutions of the dynamical Sobolev
type equation in quasi-Banach spaces.
Keywords:
quasi-Sobolev space; relatively spectral theorem; invariant spaces; exponential dichotomies of solutions; Sobolev type equations.
Received: 25.05.2015
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: Russian
Citation:
M. A. Sagadeeva, F. L. Hasan, “Existence of invariant spaces and exponential dichotomies of solutions of dynamical Sobolev type equations in quasi-Banach spaces”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:4 (2015), 46–53
\Bibitem{SagHas15}
\by M.~A.~Sagadeeva, F.~L.~Hasan
\paper Existence of invariant spaces and exponential dichotomies of solutions of dynamical Sobolev type equations in quasi-Banach spaces
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2015
\vol 7
\issue 4
\pages 46--53
\mathnet{http://mi.mathnet.ru/vyurm276}
\crossref{https://doi.org/10.14529/mmph150406}
\elib{https://elibrary.ru/item.asp?id=24389502}
Linking options:
https://www.mathnet.ru/eng/vyurm276
https://www.mathnet.ru/eng/vyurm/v7/i4/p46
This publication is cited in the following 4 articles:
E. M. Buryak, T. K. Plyshevskaya, A. B. Samarov, “Seminaru po uravneniyam sobolevskogo tipa chetvert veka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:1 (2017), 165–169
F. L. Hasan, “The bounded solutions on a semiaxis for the linearized Hoff equation in quasi-Sobolev spaces”, J. Comp. Eng. Math., 4:1 (2017), 27–37
N. N. Solovyova, S. A. Zagrebina, “Multipoint initial-final value problem for Hoff equation in quasi-Sobolev spaces”, J. Comp. Eng. Math., 4:2 (2017), 73–79
M. A. Sagadeeva, F. L. Khasan, “Ogranichennye resheniya modeli Barenblatta–Zheltova–Kochinoi v kvazisobolevykh prostranstvakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:4 (2015), 138–144
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