RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Vestnik YuUrGU. Ser. Mat. Model. Progr.: Year: Volume: Issue: Page: Find

 Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 4, Pages 113–119 (Mi vyuru293)

Short Notes

On some properties of solutions to one class of evolution Sobolev type mathematical models in quasi-Sobolev spaces

A. A. Zamyshlyaeva, D. K. T. Al-Isawi

South Ural State University, Chelyabinsk, Russian Federation

Abstract: Interest in Sobolev type equations has recently increased significantly, moreover, there arose a necessity for their consideration in quasi-Banach spaces. The need is dictated not so much by the desire to fill up the theory but by the aspiration to comprehend non-classical models of mathematical physics in quasi-Banach spaces. Notice that the Sobolev type equations are called evolutionary if solutions exist only on ${{\mathbb R}}_{{\mathbf +}}$.
The theory of holomorphic degenerate semigroups of operators constructed earlier in Banach spaces and Frechet spaces is transferred to quasi-Sobolev spaces of sequences. This article contains results about existence of the exponential dichotomies of solutions to evolution Sobolev type equation in quasi-Sobolev spaces. To obtain this result we proved the relatively spectral theorem and the existence of invariant spaces of solutions.
The article besides the introduction and references contains two paragraphs. In the first one, quasi-Banach spaces, quasi-Sobolev spaces and polynomials of Laplace quasi-operator are defined. Moreover the conditions for existence of degenerate holomorphic operator semigroups in quasi-Banach spaces of sequences are obtained. In other words, we prove the first part of the generalization of the Solomyak–Iosida theorem to quasi-Banach spaces of sequences. In the second paragraph the phase space of the homogeneous equation is constructed. Here we show the existence of invariant spaces of equation and get the conditions for exponential dichotomies of solutions.

Keywords: holomorphic degenerate semigroups; quasi-Banach spaces; quasi-Sobolev spaces; invariant space; exponential dichotomy of solution.

DOI: https://doi.org/10.14529/mmp150410

Full text: PDF file (710 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.9
MSC: 46A16, 47D03, 34D09
Language:

Citation: A. A. Zamyshlyaeva, D. K. T. Al-Isawi, “On some properties of solutions to one class of evolution Sobolev type mathematical models in quasi-Sobolev spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:4 (2015), 113–119

Citation in format AMSBIB
\Bibitem{ZamAl-15} \by A.~A.~Zamyshlyaeva, D.~K.~T.~Al-Isawi \paper On some properties of solutions to one class of evolution Sobolev type mathematical models in quasi-Sobolev spaces \jour Vestnik YuUrGU. Ser. Mat. Model. Progr. \yr 2015 \vol 8 \issue 4 \pages 113--119 \mathnet{http://mi.mathnet.ru/vyuru293} \crossref{https://doi.org/10.14529/mmp150410} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000422203200010} \elib{http://elibrary.ru/item.asp?id=24989387} 

• http://mi.mathnet.ru/eng/vyuru293
• http://mi.mathnet.ru/eng/vyuru/v8/i4/p113

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. J. K. T. Al-Isawi, “On some properties of solutions to Dzektser mathematical model in quasi-Sobolev spaces”, J. Comp. Eng. Math., 2:4 (2015), 27–36
2. M. A. Sagadeeva, “Mathematical bases of optimal measurements theory in nonstationary case”, J. Comp. Eng. Math., 3:3 (2016), 19–32
3. J. K. T. Al-Isawi, A. A. Zamyshlyaeva, “Computational experiment for one class of evolution mathematical models in quasi-Sobolev spaces”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 141–147
4. M. A. Sagadeeva, “Vyrozhdennye potoki razreshayuschikh operatorov dlya nestatsionarnykh uravnenii sobolevskogo tipa”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 9:1 (2017), 22–30
5. J. K. T. Al-Isawi, “Computational experiments for one class of mathematical models in thermodynamics and hydrodynamics”, J. Comp. Eng. Math., 4:1 (2017), 16–26
6. I. S. Strepetova, L. M. Fatkullina, G. A. Zakirova, “Spectral problems for one mathematical model of hydrodynamics”, J. Comp. Eng. Math., 4:1 (2017), 48–56
7. D. E. Shafranov, N. V. Adukova, “Solvability of the Showalter–Sidorov problem for Sobolev type equations with operators in the form of first-order polynomials from the Laplace–Beltrami operator on differential forms”, J. Comp. Eng. Math., 4:3 (2017), 27–34
•  Number of views: This page: 111 Full text: 33 References: 21