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Differ. Uravn., 2000, Volume 36, Number 12, Pages 1670–1686 (Mi de10290)  

This article is cited in 14 scientific papers (total in 14 papers)

Partial Differential Equations

Boundary Control of Oscillations at One Endpoint with the Other Endpoint Fixed in Terms of a Finite-Energy Generalized Solution of the Wave Equation

V. A. Il'inab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University

Full text: PDF file (2692 kB)

English version:
Differential Equations, 2000, 36:12, 1832–1849

Bibliographic databases:

UDC: 517.984.5
Received: 07.09.2000

Citation: V. A. Il'in, “Boundary Control of Oscillations at One Endpoint with the Other Endpoint Fixed in Terms of a Finite-Energy Generalized Solution of the Wave Equation”, Differ. Uravn., 36:12 (2000), 1670–1686; Differ. Equ., 36:12 (2000), 1832–1849

Citation in format AMSBIB
\Bibitem{Ili00}
\by V.~A.~Il'in
\paper Boundary Control of Oscillations at One Endpoint with the Other Endpoint Fixed in Terms of a Finite-Energy Generalized Solution of the Wave Equation
\jour Differ. Uravn.
\yr 2000
\vol 36
\issue 12
\pages 1670--1686
\mathnet{http://mi.mathnet.ru/de10290}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1838675}
\transl
\jour Differ. Equ.
\yr 2000
\vol 36
\issue 12
\pages 1832--1849
\crossref{https://doi.org/10.1023/A:1017508830200}


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    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. V. A. Il'in, “Boundary Control of Spherically Symmetric Oscillations of a Three-Dimensional Ball”, Proc. Steklov Inst. Math., 232 (2001), 138–149  mathnet  mathscinet  zmath
    2. A. I. Egorov, L. N. Znamenskaya, “Control of vibrations of coupled objects with distributed and lumped parameters”, Comput. Math. Math. Phys., 45:10 (2005), 1701–1718  mathnet  mathscinet  zmath
    3. V. A. Il'in, E. I. Moiseev, “Optimization of boundary controls of string vibrations”, Russian Math. Surveys, 60:6 (2005), 1093–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. A. Il'in, “Optimization of the Boundary Control of an Elastic Force at One Endpoint of a String with the Other Endpoint Fixed”, Proc. Steklov Inst. Math., 248 (2005), 111–117  mathnet  mathscinet  zmath
    5. V. A. Il'in, E. I. Moiseev, “Boundary control of string vibrations that minimizes the integral of power $p\ge1$ of the module of control or its derivative”, Autom. Remote Control, 68:2 (2007), 313–319  mathnet  crossref  mathscinet  zmath
    6. A. A. Nikitin, “Boundary control of the third boundary”, Autom. Remote Control, 68:2 (2007), 320–326  mathnet  crossref  mathscinet  zmath
    7. M. M. Potapov, “Finite-difference approximation of dirichlet observation problems for weak solutions to the wave equation subject to Robin boundary conditions”, Comput. Math. Math. Phys., 47:8 (2007), 1268–1284  mathnet  crossref  mathscinet  elib  elib
    8. V. A. Il'in, E. I. Moiseev, “Optimization of the boundary control by shift or elastic force at one end of string in a sufficiently long arbitrary time”, Autom. Remote Control, 69:3 (2008), 354–362  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. V. A. Il'in, “Optimization of the boundary control by a displacement or by an elastic force on one end of a string under a model nonlocal boundary condition”, Proc. Steklov Inst. Math., 268 (2010), 117–129  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    10. V. A. Il'in, “A terminal–boundary value problem that describes the process of damping the vibrations of a rod consisting of two segments with different densities and elasticity coefficients but with identical wave travel times”, Proc. Steklov Inst. Math., 269 (2010), 127–136  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    11. V. A. Il'in, “On the complete damping of oscillations of an inhomogeneous rod by means of a boundary control at one end”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S97–S105  mathnet  crossref  isi  elib
    12. M. M. Potapov, A. A. Dryazhenkov, “Threshold optimization in observability inequality for the wave equation with homogeneous Robin-type boundary condition”, Proc. Steklov Inst. Math., 277 (2012), 206–220  mathnet  crossref  mathscinet  isi  elib  elib
    13. M. M. Potapov, D. A. Ivanov, “Problems of two-sided boundary control for the wave equation on subcritical intervals in classes of strong generalized solutions”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 145–155  mathnet  crossref  mathscinet  isi  elib
    14. E. I. Moiseev, A. A. Kholomeeva, A. A. Frolov, “Granichnoe upravlenie smescheniem protsessom kolebanii pri granichnom uslovii tipa tormozheniya za vremya, menshee kriticheskogo”, Materialy mezhdunarodnoi konferentsiiá«InternationaláConference onáMathematicaláModellingáináAppliedáSciences, ICMMAS-17», Sankt-Peterburgskii politekhnicheskii universitet,á24ľ28 iyulyaá2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 160, VINITI RAN, M., 2019, 74–84  mathnet
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