Algebra i Analiz
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


Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find




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

Algebra i Analiz, 2023, Volume 35, Issue 1, Pages 3–32 (Mi aa1844)  
Research Papers

Shape, velocity, and exact controllability for the wave equation on a graph with cycle

S. Avdoninab, J. Edwardc, Y. Zhaob

a Moscow Center for Fundamental and Applied Mathematics, Moscow 119991, Russia
b Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775, U.S.A
c Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, U.S.A.
Full-text PDF (306 kB) First page
References:
PDF
HTML
Abstract: Exact controllability is proved on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity controllability, thereby solving their associated moment problems. This enables one to solve the moment problem associated with exact controllability. In the case of a single control, either boundary or interior, it is shown that exact controllability fails.
Keywords: control problems, dynamical method, Volterra integral equations.
Funding agency Grant number
National Science Foundation DMS 1909869
1242789
The research of Sergei Avdonin was supported in part by the National Science Foundation, grant DMS 1909869. The research of Yuanyuan Zhao was supported by the National Science Foundation Graduate Research Fellowship under Grant №1242789.
Received: 08.09.2021
English version:
St. Petersburg Mathematical Journal, 2024, Volume 35, Issue 1, Pages 1–23
DOI: https://doi.org/10.1090/spmj/1791
Bibliographic databases:
Document Type: Article
Language: English
Citation: S. Avdonin, J. Edward, Y. Zhao, “Shape, velocity, and exact controllability for the wave equation on a graph with cycle”, Algebra i Analiz, 35:1 (2023), 3–32; St. Petersburg Math. J., 35:1 (2024), 1–23
Citation in format AMSBIB
\Bibitem{AvdEdwZha23}
\by S.~Avdonin, J.~Edward, Y.~Zhao
\paper Shape, velocity, and exact controllability for the wave equation on a graph with cycle
\jour Algebra i Analiz
\yr 2023
\vol 35
\issue 1
\pages 3--32
\mathnet{http://mi.mathnet.ru/aa1844}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4403167}
\transl
\jour St. Petersburg Math. J.
\yr 2024
\vol 35
\issue 1
\pages 1--23
\crossref{https://doi.org/10.1090/spmj/1791}
Linking options:
  • https://www.mathnet.ru/eng/aa1844
  • https://www.mathnet.ru/eng/aa/v35/i1/p3
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
    Statistics & downloads:
    Abstract page:143
    Full-text PDF :1
    References:31
    First page:15
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024