RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2016, Volume 8, Issue 4, Pages 5–16 (Mi vyurm313)  

This article is cited in 2 scientific papers (total in 3 papers)

Mathematics

Nonclassical equations of mathematical physics. Linear Sobolev type equations of higher order

A. A. Zamyshlyaeva, G. A. Sviridyuk

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The article presents the review of authors' results in the field of non-classical equations of mathematical physics. The theory of Sobolev-type equations of higher order is introduced. The idea is based on generalization of degenerate operator semigroups theory in case of the following equations: decomposition of spaces, splitting of operators' actions, the construction of propagators and phase spaces for a homogeneous equation, as well as the set of valid initial values for the inhomogeneous equation. The author uses a proven phase space technology for solving Sobolev type equations consisting of reduction of a singular equation to a regular one defined on some subspace of initial space. However, unlike the first order equations, there is an extra condition that guarantees the existence of the phase space. There are some examples where the initial conditions should match together if the extra condition can't be fulfilled to solve the Cauchy problem. The reduction of nonclassical equations of mathematical physics to the initial problems for abstract Sobolev type equations of high order is conducted and justified.

Keywords: nonclassical equations of mathematical physics, the Sobolev type equations of higher order, phase space, propagators.

DOI: https://doi.org/10.14529/mmph160401

Full text: PDF file (251 kB)
References: PDF file   HTML file

UDC: 517.9
Received: 27.09.2016
Language:

Citation: A. A. Zamyshlyaeva, G. A. Sviridyuk, “Nonclassical equations of mathematical physics. Linear Sobolev type equations of higher order”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 8:4 (2016), 5–16

Citation in format AMSBIB
\Bibitem{ZamSvi16}
\by A.~A.~Zamyshlyaeva, G.~A.~Sviridyuk
\paper Nonclassical equations of mathematical physics. Linear Sobolev type equations of higher order
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2016
\vol 8
\issue 4
\pages 5--16
\mathnet{http://mi.mathnet.ru/vyurm313}
\crossref{https://doi.org/10.14529/mmph160401}
\elib{http://elibrary.ru/item.asp?id=27157543}


Linking options:
  • http://mi.mathnet.ru/eng/vyurm313
  • http://mi.mathnet.ru/eng/vyurm/v8/i4/p5

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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  mathnet  crossref  elib
    2. V. F. Chistyakov, E. V. Chistyakova, “On the concept of index for partial differential algebraic equations arising in modelling of processes in power plants”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:2 (2017), 5–23  mathnet  crossref  elib
    3. A. A. Zamyshlyaeva, A. V. Lut, “Numerical investigation of the Boussinesq–Love mathematical models on geometrical graphs”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:2 (2017), 137–143  mathnet  crossref  elib
  • Number of views:
    This page:157
    Full text:66
    References:28

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019