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J. Comp. Eng. Math., 2015, Volume 2, Issue 3, Pages 34–42 (Mi jcem19)  

This article is cited in 3 scientific papers (total in 3 papers)

Solvability of initial problems for one class of dynamical equations in quasi-Sobolev 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. Quasi-Sobolev 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 quasi-Sobolev 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 quasi-Sobolev spaces.

Keywords: Cauchy problem, Showalter Sidorov problem, Sobolev type equation, Laplase quasi-operator, 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
Language:

Citation: F. L. Hasan, “Solvability of initial problems for one class of dynamical equations in quasi-Sobolev 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 quasi-Sobolev spaces
\jour J. Comp. Eng. Math.
\yr 2015
\vol 2
\issue 3
\pages 34--42
\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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  elib
    2. 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  mathnet  crossref  mathscinet  elib
    3. 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  mathnet  crossref  mathscinet  elib
  • Journal of Computational and Engineering Mathematics
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