Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




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

Matematicheskie Zametki, 2010, Volume 87, Issue 6, Pages 803–813
DOI: https://doi.org/10.4213/mzm4744 (Mi mzm4744) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The Cauchy Problem for the Wave Equation with Lévy Laplacian

S. A. Albeverioa, Ya. I. Belopol'skayab, M. N. Fellerc

a University of Bonn, Institute for Applied Mathematics
b St. Petersburg State University of Architecture and Civil Engineering
c Ukranian Institune of Wood Machining
Full-text PDF (464 kB) Citations (4)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm4744
Abstract: We present the solution of the Cauchy problem (the initial-value problem in the whole space) for the wave equation with infinite-dimensional Lévy Laplacian $\Delta _L$,
$$ \frac{\partial^2 U(t,x)}{\partial t^2}=\Delta_LU(t,x) $$
in two function classes, the Shilov class and the Gâteaux class.
Keywords: wave equation, hyperbolic equation, Lévy Laplacian, Cauchy problem, Shilov function class, Gâteaux function class, Hilbert space, variational derivative.
Received: 12.11.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 6, Pages 787–796
DOI: https://doi.org/10.1134/S0001434610050172
Bibliographic databases:
Document Type: Article
UDC: 517.958+517.98
Language: Russian
Citation: S. A. Albeverio, Ya. I. Belopol'skaya, M. N. Feller, “The Cauchy Problem for the Wave Equation with Lévy Laplacian”, Mat. Zametki, 87:6 (2010), 803–813; Math. Notes, 87:6 (2010), 787–796
Citation in format AMSBIB
\Bibitem{AlbBelFel10}
\by S.~A.~Albeverio, Ya.~I.~Belopol'skaya, M.~N.~Feller
\paper The Cauchy Problem for the Wave Equation with L\'evy Laplacian
\jour Mat. Zametki
\yr 2010
\vol 87
\issue 6
\pages 803--813
\mathnet{http://mi.mathnet.ru/mzm4744}
\crossref{https://doi.org/10.4213/mzm4744}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2840374}
\transl
\jour Math. Notes
\yr 2010
\vol 87
\issue 6
\pages 787--796
\crossref{https://doi.org/10.1134/S0001434610050172}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000279600700017}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954419782}
Linking options:
  • https://www.mathnet.ru/eng/mzm4744
  • https://doi.org/10.4213/mzm4744
  • https://www.mathnet.ru/eng/mzm/v87/i6/p803
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025