
This article is cited in 3 scientific papers (total in 3 papers)
Solvability of initial problems for one class of dynamical equations in quasiSobolev spaces
F. L. Hasan^{} ^{} South Ural State University, Chelyabinsk, Russian Ffederation
Abstract:
The equations, which are not solved with respect to the highest derivative, are now actively studied. Such equations are also called the Sobolev type equations. Note that these equations in Banach spaces are studied quite well. QuasiSobolev spaces are quasi normalized complete spaces of sequences. Recently these spaces began to be studied. The interest to such spaces and its equations is connected with a desire to fill up the theory more than with practical applications.
The paper is devoted to the study of solvability of the Cauchy problem and the Showalter – Sidorov problem for a class of equations considered in the quasiSobolev spases. To this end we use properties of the equation operators, namely the relative boundedness of the operators. To illustrate abstract results we consider an analogue of the Hoff equation in the quasiSobolev spaces.
Keywords:
Cauchy problem, Showalter – Sidorov problem, Sobolev type equation, Laplase quasioperator, analogue of the Hoff equation.
DOI:
https://doi.org/10.14529/jcem150304
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UDC:
517.9
MSC: 47D06, 47B37, 46B45 Received: 05.09.2015
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Citation:
F. L. Hasan, “Solvability of initial problems for one class of dynamical equations in quasiSobolev spaces”, J. Comp. Eng. Math., 2:3 (2015), 34–42
Citation in format AMSBIB
\Bibitem{Has15}
\by F.~L.~Hasan
\paper Solvability of initial problems for one class of dynamical equations in quasiSobolev spaces
\jour J. Comp. Eng. Math.
\yr 2015
\vol 2
\issue 3
\pages 3442
\mathnet{http://mi.mathnet.ru/jcem19}
\crossref{https://doi.org/10.14529/jcem150304}
\elib{http://elibrary.ru/item.asp?id=24505454}
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This publication is cited in the following articles:

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

F. L. Hasan, “The bounded solutions on a semiaxis for the linearized Hoff equation in quasiSobolev spaces”, J. Comp. Eng. Math., 4:1 (2017), 27–37

N. N. Solovyova, S. A. Zagrebina, “Multipoint initialfinal value problem for Hoff equation in quasiSobolev spaces”, J. Comp. Eng. Math., 4:2 (2017), 73–79

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