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Differ. Uravn., 2000, Volume 36, Number 11, Pages 1513–1528 (Mi de10266)  

This article is cited in 22 scientific papers (total in 22 papers)

Partial Differential Equations

Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation

V. A. Il'inab

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

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English version:
Differential Equations, 2000, 36:11, 1659–1675

Bibliographic databases:

UDC: 517.984.5
Received: 10.04.2000

Citation: V. A. Il'in, “Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation”, Differ. Uravn., 36:11 (2000), 1513–1528; Differ. Equ., 36:11 (2000), 1659–1675

Citation in format AMSBIB
\by V.~A.~Il'in
\paper Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation
\jour Differ. Uravn.
\yr 2000
\vol 36
\issue 11
\pages 1513--1528
\jour Differ. Equ.
\yr 2000
\vol 36
\issue 11
\pages 1659--1675

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    Citing articles on Google Scholar: Russian citations, English citations
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    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. 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
    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. 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
    5. N. Yu. Satimov, M. Tukhtasinov, “On game problems for second-order evolution equations”, Russian Math. (Iz. VUZ), 51:1 (2007), 49–57  mathnet  crossref  mathscinet  zmath
    6. 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
    7. A. A. Nikitin, “Boundary control of the third boundary”, Autom. Remote Control, 68:2 (2007), 320–326  mathnet  crossref  mathscinet  zmath
    8. S. V. Leksina, “Zadacha granichnogo upravleniya v usloviyakh vtoroi kraevoi zadachi dlya matrichnogo volnovogo uravneniya”, Vestn. SamGU. Estestvennonauchn. ser., 2009, no. 4(70), 20–29  mathnet
    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. E. A. Kozlova, “Zadacha upravleniya dlya sistemy telegrafnykh uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(24) (2011), 162–166  mathnet  crossref
    13. E. A. Kozlova, “Zadacha o polnom uspokoenii dlya giperbolicheskogo uravneniya, soderzhaschego smeshannuyu proizvodnuyu”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(25) (2011), 37–42  mathnet  crossref
    14. E. A. Kozlova, “Zadacha upravleniya dlya giperbolicheskogo uravneniya v sluchae kharakteristik s uglovymi koeffitsientami odnogo znaka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 243–247  mathnet  crossref
    15. E. A. Kozlova, “Zadacha o polnom uspokoenii dlya odnogo klassa sistem giperbolicheskikh uravnenii vtorogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(28) (2012), 47–52  mathnet  crossref  zmath  elib
    16. 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
    17. 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
    18. E. A. Kozlova, “Zadacha granichnogo upravleniya dlya sistemy uravnenii giperbolicheskogo tipa”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:1(2) (2013), 51–56  mathnet
    19. A. A. Andreev, E. A. Kozlova, S. V. Leksina, “Granichnoe upravlenie protsessami, opisyvaemymi sistemami giperbolicheskikh uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 24–30  mathnet  crossref  adsnasa  elib
    20. N. Yu. Satimov, M. Tukhtasinov, “Evasion in a Certain Class of Distributed Control Systems”, Math. Notes, 97:5 (2015), 764–773  mathnet  crossref  crossref  mathscinet  isi  elib
    21. D. A. Ivanov, M. M. Potapov, “Approximate solution to a time optimal boundary control problem for the wave equation”, Proc. Steklov Inst. Math., 291 (2015), 102–117  mathnet  crossref  crossref  isi  elib  elib
    22. D. A. Ivanov, M. M. Potapov, “Approximations to time-optimal boundary controls for weak generalized solutions of the wave equation”, Comput. Math. Math. Phys., 57:4 (2017), 607–625  mathnet  crossref  crossref  mathscinet  isi  elib
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