Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Saratov Univ. Math. Mech. Inform.:
Year:
Volume:
Issue:
Page:
Find






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


Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, Volume 15, Issue 3, Pages 264–272
DOI: https://doi.org/10.18500/1816-9791-2015-15-3-264-272
(Mi isu592)
 

Mathematics

Homogenization of the acoustics mathematical model

A. A. Gerus, S. A. Gritsenko

Belgorod State National Research University, 85, Pobedy st., 308015, Belgorod, Russia
References:
Abstract: We consider a mathematical model of acoustics in heterogeneous medium with two different components with the common boundary. One of these is a bounded liquid domain and the other is a poroelastic medium. Poroelastic medium is perforated by pores. A pore space is filled with a viscous liquid. The motion of the liquid and the joint motion of the poroelastic media with porous space are governed by the differential equations based on the continuum mechanics laws. These equations contain rapidly oscillating terms, depending on the small parameter. The small parameter is the ratio of the average pores size to the size of domain under consideration. Rapidly oscillating terms prevent from the numerical simulations. The unique existence of the generalized solution of the boundary-value problem is proved. Homogenized equations (i.e. free from rapidly oscillating terms) are based upon the Nguetseng method of the two-scale convergence. We derived approximate models useful to the numerical calculations.
Key words: composite medium, periodic structure, Stokes equations, Lame's equations, acoustics equations, poroelastic, homogenization of periodic structures, two-scale convergence.
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. A. Gerus, S. A. Gritsenko, “Homogenization of the acoustics mathematical model”, Izv. Saratov Univ. Math. Mech. Inform., 15:3 (2015), 264–272
Citation in format AMSBIB
\Bibitem{GerGri15}
\by A.~A.~Gerus, S.~A.~Gritsenko
\paper Homogenization of the acoustics mathematical model
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 3
\pages 264--272
\mathnet{http://mi.mathnet.ru/isu592}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-3-264-272}
\elib{https://elibrary.ru/item.asp?id=24235219}
Linking options:
  • https://www.mathnet.ru/eng/isu592
  • https://www.mathnet.ru/eng/isu/v15/i3/p264
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024